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Algebra 1 : How to find the solution to an inequality with addition

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Example Questions

Example Question #41 : Equations / Inequalities

Solve this inequality:

$\displaystyle 5x -2 < 8 - x$

Possible Answers:

$x < \frac{5}{2}$ $\displaystyle x < \frac{5}{2}$

$x > \frac{5}{3}$ $\displaystyle x > \frac{5}{3}$

$x < \frac{3}{2}$ $\displaystyle x < \frac{3}{2}$

$x < \frac{7}{3}$ $\displaystyle x < \frac{7}{3}$

$x < \frac{5}{3}$ $\displaystyle x < \frac{5}{3}$

Correct answer:

$x < \frac{5}{3}$ $\displaystyle x < \frac{5}{3}$

Explanation:

First, add $\displaystyle x$ to both sides:

$\displaystyle 5x -2 +x < 8 - x + x$ , or

$\displaystyle 6x -2 < 8$ .

Then, add 2 to both sides:

$\displaystyle 6x - 2 + 2 < 8 + 2$ , or

6x < 10 $\displaystyle 6x < 10$

Finally, divide both sides by 6 to get the answer:

$x < \frac{10}{6}$ $\displaystyle x < \frac{10}{6}$

which simplifies to:

$x < \frac{5}{3}$ $\displaystyle x < \frac{5}{3}$

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Example Question #1 : How To Find The Solution To An Inequality With Addition

Solve for $\displaystyle x$ :

$\displaystyle x+3>2x-9$

Possible Answers:

x>6 $\displaystyle x>6$

x<12 $\displaystyle x< 12$

x>12 $\displaystyle x>12$

None of the other answers

x<6 $\displaystyle x< 6$

Correct answer:

x<12 $\displaystyle x< 12$

Explanation:

To solve the inequality, simply move the $\displaystyle x$ 's to one side and the integers to the other (i.e. subtract $\displaystyle x$ from both sides and add 9 to both sides). This gives you x<12 $\displaystyle x< 12$ .

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Example Question #2 : How To Find The Solution To An Inequality With Addition

Solve for $\displaystyle x$ :

$\displaystyle x+5>3x-3$

Possible Answers:

x<2 $\displaystyle x< 2$

x<4 $\displaystyle x< 4$

x<1 $\displaystyle x< 1$

x>4 $\displaystyle x>4$

x>1 $\displaystyle x>1$

Correct answer:

x<4 $\displaystyle x< 4$

Explanation:

Subtracting $\displaystyle x$ and adding 3 to both sides of the equation of $\displaystyle x+5>3x-3$ will give you 8>2x $\displaystyle 8>2x$ . Divide both sides by 2 to get x<4 $\displaystyle x< 4$ .

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Example Question #1 : How To Find The Solution To An Inequality With Addition

Which value of $\displaystyle x$ is in the solution set of the inequality $\displaystyle 2x+2>-x+17$ ?

Possible Answers:

$\displaystyle 2$

$\displaystyle 6$

$\displaystyle 5$

$\displaystyle 4$

$\displaystyle 3$

Correct answer:

$\displaystyle 6$

Explanation:

Add $\displaystyle x$ and subtract 2 from both sides of $\displaystyle 2x+2>-x+17$ to get 3x>15 $\displaystyle 3x>15$ . Then, divide both sides by 3 to get a solution of x>5 $\displaystyle x>5$ . The only answer choice that is greater than 5 is 6.

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Example Question #3 : How To Find The Solution To An Inequality With Addition

Find the solution set for $\displaystyle x$ :

$3.2 \geq -x + 0.6 > -5.1$ $\displaystyle 3.2 \geq -x + 0.6 > -5.1$

Possible Answers:

$\displaystyle [2.6, 5.7)$

$\displaystyle [-5.7, -2.6)$

$\displaystyle [-2.6, 5.7)$

$\displaystyle (-5.7, -2.6]$

$\displaystyle (-5.7, 2.6]$

Correct answer:

$\displaystyle [-2.6, 5.7)$

Explanation:

$3.2 \geq -x + 0.6 > -5.1$ $\displaystyle 3.2 \geq -x + 0.6 > -5.1$

$3.2- 0.6 \geq -x + 0.6 - 0.6 > -5.1 - 0.6$ $\displaystyle 3.2- 0.6 \geq -x + 0.6 - 0.6 > -5.1 - 0.6$

$2.6 \geq -x > -5.7$ $\displaystyle 2.6 \geq -x > -5.7$

$2.6 \cdot (-1 )\leq -x \cdot (-1 )< -5.7 \cdot (-1 )$ $\displaystyle 2.6 \cdot (-1 )\leq -x \cdot (-1 )< -5.7 \cdot (-1 )$

Note the switch in inequality symbols when the numbers are multiplied by a negative number.

$-2.6 \leq x < 5.7$ $\displaystyle -2.6 \leq x < 5.7$

or, in interval notation, $\displaystyle [-2.6, 5.7)$

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Example Question #4 : How To Find The Solution To An Inequality With Addition

Solve the inequality:

3+x-5<2 $\displaystyle 3+x-5< 2$

Possible Answers:

x<10 $\displaystyle x< 10$

No solution

x<0 $\displaystyle x< 0$

x<4 $\displaystyle x< 4$

x<-6 $\displaystyle x< -6$

Correct answer:

x<4 $\displaystyle x< 4$

Explanation:

Combine like-terms on the left side of the inequality: x-2<2 $\displaystyle x-2< 2$ . Next, isolate the variable: $x-2 \boldsymbol{+2} <2 \boldsymbol{+2}$ $\displaystyle x-2 \boldsymbol{+2} < 2 \boldsymbol{+2}$ .

Therefore the answer is x<4 $\displaystyle x< 4$ .

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Example Question #5 : How To Find The Solution To An Inequality With Addition

Solve:

$\small x+2\geq 7$ $\displaystyle \small x+2\geq 7$

Possible Answers:

$\small x> 5$ $\displaystyle \small x> 5$

$\small x\geq 5$ $\displaystyle \small x\geq 5$

$\small x< 9$ $\displaystyle \small x< 9$

None of the other answers are correct.

$\small x\leq 9$ $\displaystyle \small x\leq 9$

Correct answer:

$\small x\geq 5$ $\displaystyle \small x\geq 5$

Explanation:

Subtract 2 from each side:

$\small x+2-2\geq 7-2$ $\displaystyle \small x+2-2\geq 7-2$

$\small x\geq 5$ $\displaystyle \small x\geq 5$

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Example Question #6 : How To Find The Solution To An Inequality With Addition

Solve for $\displaystyle x$ :

2x-4 >7 $\displaystyle 2x-4 >7$

Possible Answers:

x>22 $\displaystyle x>22$

x>11 $\displaystyle x>11$

x>1.5 $\displaystyle x>1.5$

x>5.5 $\displaystyle x>5.5$

x>3.5 $\displaystyle x>3.5$

Correct answer:

x>5.5 $\displaystyle x>5.5$

Explanation:

This inequality can be solved just like an equation.

Add 4 to both sides:

2x > 11

Then divide by 2:

x > 11/2 = 5.5

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Example Question #2184 : Algebra 1

Solve the inequality:

$\small 15x - 4 \le 2x + 8 +x$ $\displaystyle \small 15x - 4 \le 2x + 8 +x$

Possible Answers:

$\small x \le1$ $\displaystyle \small x \le1$

$\small x \le \frac{4}{5}$ $\displaystyle \small x \le \frac{4}{5}$

$\small x \le \frac{6}{7}$ $\displaystyle \small x \le \frac{6}{7}$

$\small x \le \frac{11}{14}$ $\displaystyle \small x \le \frac{11}{14}$

$\small x \le 0$ $\displaystyle \small x \le 0$

Correct answer:

$\small x \le1$ $\displaystyle \small x \le1$

Explanation:

First, combine like terms on a single side of the inequality. On the right side of the inequality, combine the $\displaystyle x$ terms to obtain $\small 15x - 4 \le 3x +8$ $\displaystyle \small 15x - 4 \le 3x +8$ .

Next, we want to get all the variables on the left side of the inequality and all of the constants on the right side of the inequality. Add 4 to both sides and subtract $\displaystyle 3x$ from both sides to get $\small 12x \le 12$ $\displaystyle \small 12x \le 12$ .

Finally, to isolate the variable, divide both sides by 12 to produce the final answer, $\small x \le1$ $\displaystyle \small x \le1$ .

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Example Question #8 : How To Find The Solution To An Inequality With Addition

Solve: x-3<50 $\displaystyle x-3< 50$

Possible Answers:

$x\leq 53$ $\displaystyle x\leq 53$

x> 53 $\displaystyle x> 53$

x<53 $\displaystyle x< 53$

$x\leq 47$ $\displaystyle x\leq 47$

x<47 $\displaystyle x< 47$

Correct answer:

x<53 $\displaystyle x< 53$

Explanation:

To solve x-3<50 $\displaystyle x-3< 50$ , isolate the variable by adding three on both sides.

x-3+(3)<50+(3) $\displaystyle x-3+(3)< 50+(3)$

The correct answer is: x<53 $\displaystyle x< 53$

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Algebra 1 : How to find the solution to an inequality with addition

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #41 : Equations / Inequalities

Example Question #1 : How To Find The Solution To An Inequality With Addition

Example Question #2 : How To Find The Solution To An Inequality With Addition

Example Question #1 : How To Find The Solution To An Inequality With Addition

Example Question #3 : How To Find The Solution To An Inequality With Addition

Example Question #4 : How To Find The Solution To An Inequality With Addition

Example Question #5 : How To Find The Solution To An Inequality With Addition

Example Question #6 : How To Find The Solution To An Inequality With Addition

Example Question #2184 : Algebra 1

Example Question #8 : How To Find The Solution To An Inequality With Addition

All Algebra 1 Resources

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