solve 3 - 7(4x - 4) = -4x + 115 — step-by-step solution

Let's solve in

ℝ

3 - 7 \cdot (4 x - 4) = - 4 x + 115

ⓘ Expand using the distributive law, multiplying each term of the sum by the other factor:

- 7 \cdot (4 x - 4)

- (28 x - 28)

3 - (28 x - 28) = - 4 x + 115

ⓘ With a minus sign before parentheses, change the sign of every term inside:

- (28 x - 28)

- 28 x + 28

3 - 28 x + 28 = - 4 x + 115

ⓘ Start from

3

and move forward

28

on the number line:

3 + 28

31

31 - 28 x = - 4 x + 115

ⓘ We gather the terms in

x

on the right and the other terms on the left

31 - 115 = - 4 x + 28 x

ⓘ Start from

31

and move back

115

on the number line, going below zero:

31 - 115

-84

■Like terms are grouped by adding their coefficients:

- 4 x + 28 x

24 x

-84 = 24 x

ⓘ Divide both sides by

24

x = - \frac{84}{24}

The fraction:

\frac{84}{24}

simplifies by the common factor:

12

into the new fraction:

\frac{7}{2}

▶Solution obtained:

x = - \frac{7}{2}

The numeric value of:

x = - \frac{7}{2}

is:

▷

x = -3.5