# SOLVING FOR EXPRESSIONS

In this section, you will learn how to solve for an algebraic expression, when the value of another expression or the value of a variable is given.

Example 1 :

If 7(a + b) = 2, what is the value of (a + b)?

Solution :

7(a + b) = 2

Divde both sides by 7.

a + b = ²⁄₇

Example 2 :

If 3x + 2 = 7, find the value of 6x - 5.

Solution :

3x + 2 = 7

Subtract 2 from both sides.

3x = 5

Multiply both sides by 2.

6x = 10

Subtract 5 from both sides.

6x - 5 = 5

Example 3 :

If 5x + 5 = 3x - 3, what is the value of 4x - 9?

Solution :

5x + 5 = 3x - 3

Subtract 3x from both sides.

2x + 5 = -3

Subtract 5 from both sides.

2x = -8

Multiply both sides by 2.

4x = -16

Subtract 9 from both sides.

4x - 9 = -25

Example 4 :

Which of the following is equivalent to 2(x + 3) - 7?

(A) 2x - 2

(B) 2x - 1

(C) 2x + 1

(D) 2x + 2

Solution :

= 2(x + 3) - 7

Distribute the 2 to both terms in the parenthses, then combine the numerical constants.

= 2(x) + 2(3) - 7

= 2x + 6 - 7

= 2x - 1

The correct Answer choice is (B).

Example 5 :

Find the value of the following expression

3(5 - 3x) + 7,

if x = -2.

Solution :

= 3(5 - 3x) + 7

Substitute x = -2.

= 3[5 - 3(-2)] + 7

= 3[5 + 6] + 7

= 3(11) + 7

= 33 + 7

= 40

Example 6 :

Find the value of the following expression

a2 - b2,

if a = 3 and b = -5.

Solution :

= a2 - b2

Substitute a = 3 and b = -5.

= a2 - b2

= 32 - (-5)2

= 9 - 25

= -16

Example 7 :

If 3x + 8 = 2(y + 4), find the value of ˣ⁄y.

Solution :

3x + 8 = 2(y + 4)

Distribute the 2 to both terms in the parenthses.

3x + 8 = 2(y) + 2(4)

3x + 8 = 2y + 8

Subtract 8 from both sides.

3x = 2y

Divide both sides by y.

³ˣ⁄y = 2

Multiply both sides by .

(³ˣ⁄y)() = 2()

ˣ⁄y =

Example 8 :

If ²ᵐ⁄n = ﻿⅗﻿, what is the value of ⁿ⁄m?

Solution :

²ᵐ⁄n =

Multiply both sides by ½.

(½)(²ᵐ⁄n) = (½)()

ᵐ⁄n = ³⁄₁₀

Take reciprocal on both sides.

ⁿ⁄m = ¹⁰⁄₃

Example 9 :

When 6 times the number n is added to 8, the result is 2. What number results when 3 times n is added to 4?

Solution :

From the given information,

6n + 8 = 2

Subtract 8 from both sides.

6n = -6

Divide both sides by 2.

3n = -3

3n + 4 = 1

Adding 4 to 3 times n results 1.

Example 10 :

Subtracting 15 from 14 times of the number k results 13. If 5 is subtracted from 7 times k, what is the result?

Solution :

From the given information,

14k - 15 = 13

14k = 28

Divide both sides by 2.

7k = 14

Subtract 5 from both sides.

7k - 5 = 9

Subtracting 5 from 7 times k results 9.

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