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Math  /  Algebra

QuestionSolve the following equation. Check your solution. 0.70x+0.05(6−x)=0.10(107)0.70 x+0.05(6-x)=0.10(107)
The solution set is □\square B.

Studdy Solution

STEP 1

1. The equation 0.70x+0.05(6−x)=0.10(107)0.70x + 0.05(6-x) = 0.10(107) is a linear equation in one variable.
2. The goal is to solve for xx.
3. The equation involves basic operations such as distribution, combining like terms, and solving linear equations.

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Isolate the variable xx.
3. Check the solution by substituting it back into the original equation.

STEP 3

Distribute 0.050.05 in the term 0.05(6−x)0.05(6-x):
0.70x+0.05⋅6−0.05⋅x=0.10⋅107 0.70x + 0.05 \cdot 6 - 0.05 \cdot x = 0.10 \cdot 107
This simplifies to:
0.70x+0.30−0.05x=10.7 0.70x + 0.30 - 0.05x = 10.7

STEP 4

Combine like terms on the left side of the equation:
(0.70x−0.05x)+0.30=10.7 (0.70x - 0.05x) + 0.30 = 10.7
This simplifies to:
0.65x+0.30=10.7 0.65x + 0.30 = 10.7

STEP 5

Subtract 0.300.30 from both sides to isolate the term with xx:
0.65x=10.7−0.30 0.65x = 10.7 - 0.30
Simplify the right side:
0.65x=10.4 0.65x = 10.4

STEP 6

Divide both sides by 0.650.65 to solve for xx:
x=10.40.65 x = \frac{10.4}{0.65}
Calculate the division:
x=16 x = 16

STEP 7

Check the solution by substituting x=16x = 16 back into the original equation:
0.70(16)+0.05(6−16)=0.10(107) 0.70(16) + 0.05(6-16) = 0.10(107)
Calculate each term:
11.2+0.05(−10)=10.7 11.2 + 0.05(-10) = 10.7
Simplify:
11.2−0.5=10.7 11.2 - 0.5 = 10.7
10.7=10.7 10.7 = 10.7
Both sides are equal, confirming the solution is correct.
The solution set is 16\boxed{16} B.

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