(3x-4)/(-14)=9/10 — step-by-step solution

1) Let's solve in

ℝ

\frac{3 x - 4}{-14} = \frac{9}{10}

ⓘ The sign of a fraction goes in front of the bar, whether it comes from the numerator or the denominator:

\frac{3 x - 4}{-14}

- \frac{3 x - 4}{14}

- \frac{3 x - 4}{14} = \frac{9}{10}

ⓘ The minus sign of the fraction goes into the numerator or the denominator, changing the sign of each of its terms:

- \frac{3 x - 4}{14}

\frac{- 3 x + 4}{14}

\frac{- 3 x + 4}{14} = \frac{9}{10}

- 3 x + 4 = \frac{9}{10} \cdot 14

ⓘ Multiplying a fraction by a number multiplies its numerator:

\frac{9}{10} \cdot 14

\frac{9 \cdot 14}{10}

\frac{126}{10}

- 3 x + 4 = \frac{126}{10}

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

2

, their greatest common divisor:

\frac{126}{10}

\frac{63 \cdot 2}{5 \cdot 2}

\frac{63}{5}

- 3 x + 4 = \frac{63}{5}

ⓘ We gather the terms in

x

on the right and the other terms on the left

4 - \frac{63}{5} = 3 x

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

4 - \frac{63}{5}

\frac{5 \cdot 4 - 63}{5}

\frac{5 \cdot 4 - 63}{5} = 3 x

ⓘ Multiplications are done before additions and subtractions:

5 \cdot 4

20

\frac{20 - 63}{5} = 3 x

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

20 - 63

-43

- \frac{43}{5} = 3 x

ⓘ Both sides are divided by

3

x = - \frac{\frac{43}{5}}{3}

ⓘ Dividing a fraction by

3

is multiplying its denominator by

3

- \frac{\frac{43}{5}}{3}

- \frac{43}{5 \cdot 3}

x = - \frac{43}{5 \cdot 3}

ⅰ

5 \cdot 3

15

▶Solution found:

x = - \frac{43}{15}

2) The numeric value of:

x = - \frac{43}{15}

is:

▷

x = \approx -2.8667