Question

question 10. solve the following equation for x. round the answer to the nearest hundredth. 0.5(10x + 22) = 2.8(0.2x + 5) a. 0.54 b. 0.68 c. 3.15 d. 1.48

Explanation:

Step1: Expand both sides

Using the distributive property ($a(b + c) = ab + ac$), we expand the left - hand side: $0.5(10x + 22)=0.5\times10x+0.5\times22 = 5x+11$.
We expand the right - hand side: $2.8(0.2x + 5)=2.8\times0.2x+2.8\times5=0.56x + 14$.
So the equation becomes $5x + 11=0.56x+14$.

Step2: Move like terms together

Subtract $0.56x$ from both sides: $5x-0.56x + 11=0.56x-0.56x + 14$, which simplifies to $4.44x+11 = 14$.
Then subtract 11 from both sides: $4.44x+11 - 11=14 - 11$, so $4.44x=3$.

Step3: Solve for x

Divide both sides by 4.44: $x=\frac{3}{4.44}\approx0.68$.

Answer:

B. 0.68