3(3x+1)=9-5(3x-3) — step-by-step solution

Let's solve in

ℝ

3 \cdot (3 x + 1) = 9 - 5 \cdot (3 x - 3)

ⓘ Expand by multiplying each term inside the parentheses:

3 \cdot (3 x + 1)

9 x + 3

- 5 \cdot (3 x - 3)

- (15 x - 15)

9 x + 3 = 9 - (15 x - 15)

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

- (15 x - 15)

- 15 x + 15

9 x + 3 = 9 - 15 x + 15

ⓘ Start from

9

and move forward

15

on the number line:

9 + 15

24

9 x + 3 = 24 - 15 x

ⓘ We subtract

3

from both sides■Start from

24

and move back

3

on the number line:

24 - 3

21

9 x = 21 - 15 x

ⓘ We add

15 x

to both sides

9 x + 15 x = 21

ⓘ Like terms are grouped by adding their coefficients:

9 x + 15 x

24 x

24 x = 21

ⓘ Both sides are divided by

24

x = \frac{21}{24}

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

3

, their greatest common divisor:

\frac{21}{24}

\frac{7 \cdot 3}{8 \cdot 3}

\frac{7}{8}

▶Solution obtained:

x = \frac{7}{8}

The numeric value of:

x = \frac{7}{8}

is:

▷

x = 0.875