13. $\\frac{1}{3}(24x - 54)=11(x - 4)+5$
13. $\\frac{1}{3}(24x - 54)=11(x - 4)+5$
Answer
Explanation:
Step1: Expand both sides of the equation
Use the distributive property (a(b + c)=ab+ac). For the left - hand side: (\frac{1}{3}(24x - 54)=\frac{1}{3}\times24x-\frac{1}{3}\times54 = 8x-18). For the right - hand side: (11(x - 4)+5=11x-44 + 5=11x-39). The equation becomes (8x-18=11x-39).
Step2: Move the terms with (x) to one side and constants to the other side
Subtract (8x) from both sides: (8x-18-8x=11x-39 - 8x), which simplifies to (-18 = 3x-39). Then add (39) to both sides: (-18 + 39=3x-39+39). We get (21 = 3x).
Step3: Solve for (x)
Divide both sides by (3): (\frac{21}{3}=\frac{3x}{3}).
Answer:
(x = 7)