How to solve 5x+3=(4)/(3)(1+x)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 5x+3=(4)/(3)(1+x) | Equatix

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Question

$$5x+3= \frac{ 4 }{ 3 } (1+x)$$

Solve for x

$x=-\frac{5}{11}\approx -0.454545455$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{4}{3}$ by $1+x$.

$$5x+3=\frac{4}{3}+\frac{4}{3}x$$

Subtract $\frac{4}{3}x$ from both sides.

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

Combine $5x$ and $-\frac{4}{3}x$ to get $\frac{11}{3}x$.

$$\frac{11}{3}x+3=\frac{4}{3}$$

Subtract $3$ from both sides.

$$\frac{11}{3}x=\frac{4}{3}-3$$

Convert $3$ to fraction $\frac{9}{3}$.

$$\frac{11}{3}x=\frac{4}{3}-\frac{9}{3}$$

Since $\frac{4}{3}$ and $\frac{9}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{3}x=\frac{4-9}{3}$$

Subtract $9$ from $4$ to get $-5$.

$$\frac{11}{3}x=-\frac{5}{3}$$

Multiply both sides by $\frac{3}{11}$, the reciprocal of $\frac{11}{3}$.

$$x=-\frac{5}{3}\times \frac{3}{11}$$

Multiply $-\frac{5}{3}$ times $\frac{3}{11}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\times 3}{3\times 11}$$

Cancel out $3$ in both numerator and denominator.

$$x=\frac{-5}{11}$$

Fraction $\frac{-5}{11}$ can be rewritten as $-\frac{5}{11}$ by extracting the negative sign.

$$x=-\frac{5}{11}$$

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