2(1-x)=3(1+2x)+5 — step-by-step solution

Let's solve in

ℝ

2 \cdot (1 - x) = 3 \cdot (1 + 2 x) + 5

ⓘ Expand by multiplying each term inside the parentheses:

2 \cdot (1 - x)

2 + 2 \cdot (- x)

3 \cdot (1 + 2 x)

3 + 6 x

2 + 2 \cdot (- x) = 3 + 6 x + 5

ⓘ The minus sign is placed in front of the product:

2 \cdot (- x)

- 2 x

■Start from

3

and move forward

5

on the number line:

3 + 5

8

2 - 2 x = 8 + 6 x

ⓘ We gather the terms in

x

on the right and the other terms on the left

2 - 8 = 6 x + 2 x

ⓘ Start from

2

and move back

8

on the number line, going below zero:

2 - 8

-6

■Like terms are grouped by adding their coefficients:

6 x + 2 x

8 x

-6 = 8 x

ⓘ Both sides are divided by

8

x = - \frac{6}{8}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

- \frac{6}{8}

- \frac{3 \cdot 2}{4 \cdot 2}

- \frac{3}{4}

▶Solution obtained:

x = - \frac{3}{4}

The numeric value of:

x = - \frac{3}{4}

equals:

▷

x = -0.75