7-(2x+9)=11x-5(1-x) — step-by-step solution

1) Let's solve in

ℝ

7 - (2 x + 9) = 11 x - 5 \cdot (1 - x)

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (2 x + 9)

- 2 x - 9

7 - 2 x - 9 = 11 x - 5 \cdot (1 - x)

ⓘ Start from

7

and move back

9

on the number line, going below zero:

7 - 9

-2

- 2 - 2 x = 11 x - 5 \cdot (1 - x)

ⓘ Expand by multiplying each term inside the parentheses:

- 5 \cdot (1 - x)

- (5 + 5 \cdot (- x))

- 2 - 2 x = 11 x - (5 + 5 \cdot (- x))

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (5 + 5 \cdot (- x))

- 5 - 5 \cdot (- x)

- 2 - 2 x = 11 x - 5 - 5 \cdot (- x)

ⓘ Two minus signs cancel out:

-5 \cdot (- x)

5 x

- 2 - 2 x = 11 x - 5 + 5 x

ⓘ Like terms are grouped by adding their coefficients:

11 x + 5 x

16 x

- 2 - 2 x = 16 x - 5

ⓘ We gather the terms in

x

on the right and the other terms on the left

- 2 + 5 = 16 x + 2 x

ⓘ Start from

-2

and move forward

5

on the number line, going past zero:

- 2 + 5

3

■Like terms are grouped by adding their coefficients:

16 x + 2 x

18 x

3 = 18 x

ⓘ Both sides are divided by

18

x = \frac{3}{18}

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

3

, their greatest common divisor:

\frac{3}{18}

\frac{1 \cdot 3}{6 \cdot 3}

\frac{1}{6}

▶Solution obtained:

x = \frac{1}{6}

2) The numeric value of:

x = \frac{1}{6}

equals:

▷

x = \approx 0.1667