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$Solve for \(x\): (3)/(4)x-(3)/(4) >= -6$

Solve for $x$ : $\frac{3}{4}x-\frac{3}{4} \geq -6$

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Multiplication with rational exponents

Full solution

Q. Solve for

x

:

\frac{3}{4}x-\frac{3}{4} \geq -6

Isolate variable term: Step $1$ : Isolate the variable term on one side. $\newline$ Add $(\frac{3}{4})$ to both sides to eliminate the constant term on the left side. $\newline$ $(\frac{3}{4})x - (\frac{3}{4}) + (\frac{3}{4}) \geq -6 + (\frac{3}{4})$
Simplify both sides: Step $2$ : Simplify both sides. $\newline$ $(\frac{3}{4})x \geq -6 + (\frac{3}{4})$
Convert $-6$ to fraction: Step $3$ : Convert $-6$ to a fraction with the same denominator as $(3/4)$ to simplify addition. $\newline$ $-6 = -24/4$ $\newline$ Now, add $-24/4$ and $3/4$ . $\newline$ $-24/4 + 3/4 = -21/4$
Solve for x: Step $4$ : Now, solve for x. $\newline$ $(\frac{3}{4})x \geq -\frac{21}{4}$ $\newline$ To isolate x, divide both sides by $(\frac{3}{4})$ . $\newline$ $x \geq (\frac{-21}{4}) / (\frac{3}{4})$
Final solution: Step $5$ : Simplify the division of fractions by multiplying by the reciprocal. $\newline$ $x \geq \frac{-21}{4} \times \frac{4}{3}$ $\newline$ $x \geq \frac{-21}{3}$ $\newline$ $x \geq -7$

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