4(x-4)=14-6(4x+1) — step-by-step solution

Let's solve in

ℝ

4 \cdot (x - 4) = 14 - 6 \cdot (4 x + 1)

ⓘ Expand by multiplying each term inside the parentheses:

4 \cdot (x - 4)

4 x - 16

- 6 \cdot (4 x + 1)

- (24 x + 6)

4 x - 16 = 14 - (24 x + 6)

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

- (24 x + 6)

- 24 x - 6

4 x - 16 = 14 - 24 x - 6

ⓘ Start from

14

and move back

6

on the number line:

14 - 6

8

4 x - 16 = 8 - 24 x

ⓘ We add

16

to both sides■Start from

8

and move forward

16

on the number line:

8 + 16

24

4 x = 24 - 24 x

ⓘ We add

24 x

to both sides

4 x + 24 x = 24

ⓘ Like terms are grouped by adding their coefficients:

4 x + 24 x

28 x

28 x = 24

ⓘ Both sides are divided by

28

x = \frac{24}{28}

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

4

, their greatest common divisor:

\frac{24}{28}

\frac{6 \cdot 4}{7 \cdot 4}

\frac{6}{7}

▶Solution obtained:

x = \frac{6}{7}

The numeric value of:

x = \frac{6}{7}

equals:

▷

x = \approx 0.8571