Solve for g. Give an exact answer. 10(0.4 + 0.5g) = 4g
The Correct Answer and Explanation is:
10(0.4+0.5g)=4g
Step 1: Distribute the 10 on the left side
Apply the distributive property:10⋅0.4+10⋅0.5g=4g10 \cdot 0.4 + 10 \cdot 0.5g = 4g10⋅0.4+10⋅0.5g=4g4+5g=4g4 + 5g = 4g4+5g=4g
Step 2: Move all terms to one side
Subtract 4g4g4g from both sides to get all ggg terms on one side:4+5g−4g=04 + 5g – 4g = 04+5g−4g=04+g=04 + g = 04+g=0
Step 3: Solve for ggg
Subtract 4 from both sides:g=−4g = -4g=−4
Final Answer:
g=−4\boxed{g = -4}g=−4
Explanation:
This problem is a linear equation in one variable. The goal is to isolate the variable ggg and solve for its exact value.
We start by using the distributive property, which allows us to eliminate parentheses by multiplying the number outside (in this case, 10) with each term inside the parentheses. That turns the left-hand side of the equation into two terms: 10×0.4=410 \times 0.4 = 410×0.4=4 and 10×0.5g=5g10 \times 0.5g = 5g10×0.5g=5g. So we simplify the expression to:4+5g=4g4 + 5g = 4g4+5g=4g
Next, we aim to get all terms involving ggg on one side. To do this, subtract 4g4g4g from both sides:4+g=04 + g = 04+g=0
Now, we isolate ggg by subtracting 4 from both sides:g=−4g = -4g=−4
This is the solution. It’s important to check your answer to confirm accuracy. Substituting g=−4g = -4g=−4 back into the original equation:10(0.4+0.5(−4))=10(0.4−2)=10(−1.6)=−1610(0.4 + 0.5(-4)) = 10(0.4 – 2) = 10(-1.6) = -1610(0.4+0.5(−4))=10(0.4−2)=10(−1.6)=−16
On the right side:4(−4)=−164(-4) = -164(−4)=−16
Both sides equal −16-16−16, so our solution g=−4g = -4g=−4 is correct.
This equation showcases the importance of distributive property and simple algebraic manipulation, which are foundational in solving real-world and mathematical problems involving unknowns.
