5|3+7m|+1=51 — step-by-step solution

1) Let's solve in

ℝ

5 \cdot | 3 + 7 m | + 1 = 51

ⓘ We subtract

1

from both sides

5 \cdot | 3 + 7 m | = 51 - 1

ⓘ Start from

51

and move back

1

on the number line:

51 - 1

50

5 \cdot | 3 + 7 m | = 50

Since

5 \neq 0

, divide both sides by

5

| 3 + 7 m | = 10

Since

10 \geq 0

| 3 + 7 m | = 10

is equivalent to

3 + 7 m = 10

3 + 7 m = -10

2) Let's solve in

ℝ

3 + 7 m = 10

ⓘ We subtract

3

from both sides

7 m = 10 - 3

ⓘ Start from

10

and move back

3

on the number line:

10 - 3

7

7 m = 7

ⓘ Both sides are divided by

7

m = \frac{7}{7}

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

7

, their greatest common divisor:

\frac{7}{7}

1

Solution found:

m = 1

3) Let's solve in

ℝ

3 + 7 m = -10

ⓘ We subtract

3

from both sides

7 m = - 10 - 3

ⓘ Start from

-10

and move back

3

more on the number line, away from zero:

- 10 - 3

-13

7 m = -13

ⓘ Both sides are divided by

7

Solution obtained:

m = - \frac{13}{7}

▶Solution:

m = {- \frac{13}{7}, 1}

4) The numeric value of:

m = {- \frac{13}{7}, 1}

equals:

▷

m = {\approx -1.8571, 1}