7(2a+4)=6(5a-3)+10 — step-by-step solution

Let's solve in

ℝ

7 \cdot (2 a + 4) = 6 \cdot (5 a - 3) + 10

ⓘ Expand by multiplying each term inside the parentheses:

7 \cdot (2 a + 4)

14 a + 28

6 \cdot (5 a - 3)

30 a - 18

14 a + 28 = 30 a - 18 + 10

ⓘ Start from

-18

and move forward

10

on the number line, getting closer to zero:

- 18 + 10

-8

14 a + 28 = 30 a - 8

ⓘ We gather the terms in

a

on the right and the other terms on the left

28 + 8 = 30 a - 14 a

ⓘ Start from

28

and move forward

8

on the number line:

28 + 8

36

■Like terms are grouped by adding their coefficients:

30 a - 14 a

16 a

36 = 16 a

ⓘ Both sides are divided by

16

a = \frac{36}{16}

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

4

, their greatest common divisor:

\frac{36}{16}

\frac{9 \cdot 4}{4 \cdot 4}

\frac{9}{4}

▶Solution found:

a = \frac{9}{4}

The numeric value of:

a = \frac{9}{4}

is:

▷

a = 2.25