Solve for x. (-4)/(3)+(3x+7)/(12)=1 Answer:

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. The common denominator for 3 and 12 is 12.Rewrite Fractions: Rewrite each fraction with the common denominator of 12. (-4)/(3) becomes (-4 * 4)/(3 * 4) = -16/12 (3x+7)/(12) remains the same since its denominator is already 12.Combine Fractions: Combine the fractions on the left side of the equation. (-16/12) + (3x+7)/12 = (-16 + 3x + 7)/12Simplify Numerator: Simplify the numerator of the combined fraction. -16 + 3x + 7 = 3x - 9 So, (3x - 9)/12 = 1Multiply by 12: Multiply both sides of the equation by 12 to eliminate the denominator. (3x - 9)/12 * 12 = 1 * 12 3x - 9 = 12Add 9: Add 9 to both sides of the equation to isolate the term with x. 3x - 9 + 9 = 12 + 9 3x = 21Divide by 3: Divide both sides of the equation by 3 to solve for x. 3x / 3 = 21 / 3 x = 7

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Grade 8

Negative Exponents

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Q. Solve for

\mathrm{x}

\newline

\frac{-4}{3}+\frac{3 x+7}{12}=1

\newline

Answer:

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. $\newline$ The common denominator for $3$ and $12$ is $12$ .
Rewrite Fractions: Rewrite each fraction with the common denominator of $12$ . $\frac{-4}{3}$ becomes $\frac{-4 \times 4}{3 \times 4} = \frac{-16}{12}$ $\frac{3x+7}{12}$ remains the same since its denominator is already $12$ .
Combine Fractions: Combine the fractions on the left side of the equation. $\newline$ $(-\frac{16}{12}) + \frac{3x+7}{12} = \frac{-16 + 3x + 7}{12}$
Simplify Numerator: Simplify the numerator of the combined fraction. $\newline$ $-16 + 3x + 7 = 3x - 9$ $\newline$ So, $(3x - 9)/12 = 1$
Multiply by $12$ : Multiply both sides of the equation by $12$ to eliminate the denominator. $\newline$ $(3x - 9)/12 \times 12 = 1 \times 12$ $\newline$ $3x - 9 = 12$
Add $9$ : Add $9$ to both sides of the equation to isolate the term with $x$ . $\newline$ $3x - 9 + 9 = 12 + 9$ $\newline$ $3x = 21$
Divide by $3$ : Divide both sides of the equation by $3$ to solve for $x$ . $\frac{3x}{3} = \frac{21}{3}$ $x = 7$