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SSAT Middle Level Math : How to subtract variables

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Example Questions

Example Question #1 : How To Subtract Variables

Simplify: $\displaystyle (3x+6) - (8x-4)$

Possible Answers:

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

-5x+10 $\displaystyle -5x+10$

-11x+2 $\displaystyle -11x+2$

11x+2 $\displaystyle 11x+2$

11x+10 $\displaystyle 11x+10$

Correct answer:

-5x+10 $\displaystyle -5x+10$

Explanation:

$\displaystyle (3x+6) - (8x-4) = (3x-8x) +[6-(-4)]= -5x +10$

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Example Question #2 : How To Subtract Variables

Simplify: $\displaystyle (3x+6) - (9x-5)$

Possible Answers:

-6x+11 $\displaystyle -6x+11$

-12x+11 $\displaystyle -12x+11$

-12x+1 $\displaystyle -12x+1$

-6x-11 $\displaystyle -6x-11$

-6x+1 $\displaystyle -6x+1$

Correct answer:

-6x+11 $\displaystyle -6x+11$

Explanation:

$\displaystyle (3x+6) - (9x-5) = (3x-9x)+[6-(-5)] = -6x +11$

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Example Question #3 : How To Subtract Variables

Simplify:

$\displaystyle 18x - 5 (x - 7)$

Possible Answers:

48x $\displaystyle 48x$

13x + 7 $\displaystyle 13x + 7$

13x+ 35 $\displaystyle 13x+ 35$

13x - 7 $\displaystyle 13x - 7$

$\displaystyle 13x - 35$

Correct answer:

13x+ 35 $\displaystyle 13x+ 35$

Explanation:

$\displaystyle 18x - 5 (x - 7)$

$= 18x - 5 \cdot x - (- 5) \cdot 7$ $\displaystyle = 18x - 5 \cdot x - (- 5) \cdot 7$

$\displaystyle = 18x - 5x - (- 35)$

$\displaystyle = (18 - 5)x + 35$

$\displaystyle = 13x + 35$

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Example Question #71 : Variables

Simplify:

$\displaystyle 78 - 6 (x - 8)$

Possible Answers:

$\displaystyle -6x - 30$

$\displaystyle -6x + 86$

$\displaystyle -6x + 70$

$\displaystyle -6x + 30$

$\displaystyle -6x + 126$

Correct answer:

$\displaystyle -6x + 126$

Explanation:

$\displaystyle 78 - 6 (x - 8)$

$= 78 - 6 \cdot x - (- 6) \cdot 8$ $\displaystyle = 78 - 6 \cdot x - (- 6) \cdot 8$

$\displaystyle = 78 - 6x + 48$

$\displaystyle = - 6x + 78 + 48$

$\displaystyle = - 6x + 126$

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Example Question #4 : How To Subtract Variables

Solve for $\displaystyle x$ :

$\displaystyle 4 + x = 11$

Possible Answers:

x=4 $\displaystyle x=4$

x=11 $\displaystyle x=11$

x=5 $\displaystyle x=5$

x=7 $\displaystyle x=7$

x=6 $\displaystyle x=6$

Correct answer:

x=7 $\displaystyle x=7$

Explanation:

In order to solve for $\displaystyle x$ , move $\displaystyle x$ to one side of the equation and everything else to the other. To do this, subtract $\displaystyle 4$ from both sides.

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Example Question #5 : How To Subtract Variables

Simplify:

$\displaystyle 5(b-3)-3(2b+4)$

Possible Answers:

b-27 $\displaystyle b-27$

$-b^{2}-27$ $\displaystyle -b^{2}-27$

-b-27 $\displaystyle -b-27$

-b+27 $\displaystyle -b+27$

b+27 $\displaystyle b+27$

Correct answer:

-b-27 $\displaystyle -b-27$

Explanation:

The first step is to apply the distributive property. Don't forget to distribute the negative in the second parenthesis!

$\displaystyle 5(b-3)-3(2b+4)$

$(5\times b)-(5\times3)+(-3\times2b)+(-3\times4)$ $\displaystyle (5\times b)-(5\times3)+(-3\times2b)+(-3\times4)$

$\displaystyle 5b-15-6b-12$

Next, combine the variables and the numbers. This gives us:

$\displaystyle 5b-6b-15-12$

-b-27 $\displaystyle -b-27$

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Example Question #72 : Variables

Which of the following phrases can be written as the algebraic expression $\frac{1}{5} - 6x$ $\displaystyle \frac{1}{5} - 6x$ ?

Possible Answers:

One fifth less than the product of six and a number

Six less than one fifth of a number

None of the other responses is correct.

One fifth decreased by the product of six and a number

One fifth the product of negative six and a number

Correct answer:

One fifth decreased by the product of six and a number

Explanation:

$\frac{1}{5} - 6x$ $\displaystyle \frac{1}{5} - 6x$ is one fifth decreased by $\displaystyle 6x$ . $\displaystyle 6x$ is the product of six and a number.

Consequently, $\frac{1}{5} - 6x$ $\displaystyle \frac{1}{5} - 6x$ is "one fifth decreased by the product of six and a number".

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Example Question #73 : Variables

Which of the following phrases can be written as the algebraic expression $\frac{x-9}{13}$ $\displaystyle \frac{x-9}{13}$ ?

Possible Answers:

The correct answer is not among the other choices.

Thirteen divided by the difference of a number and nine.

Thirteen divided into the difference of a number and nine.

Thirteen divided into the difference of nine and a number.

Thirteen divided by the difference of nine and a number.

Correct answer:

Thirteen divided into the difference of a number and nine.

Explanation:

$\frac{x-9}{13}$ $\displaystyle \frac{x-9}{13}$ is thirteen divided into x - 9 $\displaystyle x - 9$ .

x - 9 $\displaystyle x - 9$ is the difference of a number and nine.

Therefore,

$\frac{x-9}{13}$ $\displaystyle \frac{x-9}{13}$ is "thirteen divided into the difference of a number and nine".

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Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

$\displaystyle 14x - 5 (x + 8)$

Possible Answers:

9x -40 $\displaystyle 9x -40$

9x+ 40 $\displaystyle 9x+ 40$

$\displaystyle x$

9x - 8 $\displaystyle 9x - 8$

9x + 8 $\displaystyle 9x + 8$

Correct answer:

9x -40 $\displaystyle 9x -40$

Explanation:

$\displaystyle 14x - 5 (x + 8)$

$= 14x - 5 \cdot x - 5 \cdot 8$ $\displaystyle = 14x - 5 \cdot x - 5 \cdot 8$

$\displaystyle = 14x - 5x - 40$

$\displaystyle = (14- 5) x - 40$

$\displaystyle = 9x - 40$

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Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

$\displaystyle 8 (x - 7) - 3(x + 2)$

Possible Answers:

$\displaystyle 11x - 62$

5x-9 $\displaystyle 5x-9$

$\displaystyle 5 x - 50$

$\displaystyle 5 x - 62$

11x-9 $\displaystyle 11x-9$

Correct answer:

$\displaystyle 5 x - 62$

Explanation:

$\displaystyle 8 (x - 7) - 3(x + 2)$

$= 8 \cdot x -8 \cdot 7 - 3 \cdot x + (-3) \cdot 2$ $\displaystyle = 8 \cdot x -8 \cdot 7 - 3 \cdot x + (-3) \cdot 2$

$\displaystyle = 8x -56 - 3 x -6$

$\displaystyle = 8x - 3 x -56 -6$

$\displaystyle =( 8 - 3 ) x - (56 + 6)$

$\displaystyle =5 x - 62$

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SSAT Middle Level Math : How to subtract variables

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : How To Subtract Variables

Example Question #2 : How To Subtract Variables

Example Question #3 : How To Subtract Variables

Example Question #71 : Variables

Example Question #4 : How To Subtract Variables

Example Question #5 : How To Subtract Variables

Example Question #72 : Variables

Example Question #73 : Variables

Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

All SSAT Middle Level Math Resources

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