(7x)/3+2= 1/3 — step-by-step solution

1) Let's solve in

ℝ

\frac{7 x}{3} + 2 = \frac{1}{3}

ⓘ We subtract

2

from both sides

\frac{7 x}{3} = \frac{1}{3} - 2

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{1}{3} - 2

\frac{1 - 2 \cdot 3}{3}

\frac{7 x}{3} = \frac{1 - 2 \cdot 3}{3}

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 3

6

\frac{7 x}{3} = \frac{1 - 6}{3}

ⓘ The numerator and the denominator are computed before the division:

1 - 6

-5

\frac{7 x}{3} = - \frac{5}{3}

ⓘ We multiply both sides by

3

7 x = 3 \cdot (- \frac{5}{3})

ⓘ Both sides are divided by

7

x = \frac{3 \cdot (- \frac{5}{3})}{7}

ⓘ The minus sign is placed in front of the product:

3 \cdot (- \frac{5}{3})

- 3 \cdot \frac{5}{3}

x = - \frac{3 \cdot \frac{5}{3}}{7}

ⓘ Multiplying a fraction by a number multiplies its numerator:

3 \cdot \frac{5}{3}

\frac{3 \cdot 5}{3}

\frac{15}{3}

x = - \frac{\frac{15}{3}}{7}

ⓘ Dividing a fraction by

7

is multiplying its denominator by

7

- \frac{\frac{15}{3}}{7}

- \frac{15}{3 \cdot 7}

■A fraction is simplified by dividing the numerator and the denominator by the same number:

- \frac{15}{3 \cdot 7}

- \frac{5}{7}

▶Solution obtained:

x = - \frac{5}{7}

2) The numeric value of:

x = - \frac{5}{7}

equals:

▷

x = \approx -0.7143