QuestionJuly 16, 2025

Solve the equation, and check the solution. (1)/(4)(3x+5)-(1)/(5)(x+7)=7

Solve the equation, and check the solution. (1)/(4)(3x+5)-(1)/(5)(x+7)=7
Solve the equation, and check the solution.
(1)/(4)(3x+5)-(1)/(5)(x+7)=7

Solution
3.1(212 votes)

Answer

x = \frac{143}{11} Explanation 1. Eliminate Fractions Multiply the entire equation by 20 (LCM of 4 and 5) to eliminate fractions: 20 \cdot \frac{1}{4}(3x+5) - 20 \cdot \frac{1}{5}(x+7) = 20 \cdot 7. 2. Simplify Equation Simplify each term: 5(3x + 5) - 4(x + 7) = 140. 3. Distribute Terms Distribute the constants: 15x + 25 - 4x - 28 = 140. 4. Combine Like Terms Combine like terms: 11x - 3 = 140. 5. Solve for x Add 3 to both sides: 11x = 143. Then divide by 11: x = \frac{143}{11}. 6. Verify Solution Substitute x = \frac{143}{11} back into the original equation to verify: \frac{1}{4}(3(\frac{143}{11})+5)-\frac{1}{5}(\frac{143}{11}+7)=7. Simplifying confirms the solution is correct.

Explanation

1. Eliminate Fractions<br /> Multiply the entire equation by 20 (LCM of 4 and 5) to eliminate fractions: $20 \cdot \frac{1}{4}(3x+5) - 20 \cdot \frac{1}{5}(x+7) = 20 \cdot 7$.<br /><br />2. Simplify Equation<br /> Simplify each term: $5(3x + 5) - 4(x + 7) = 140$.<br /><br />3. Distribute Terms<br /> Distribute the constants: $15x + 25 - 4x - 28 = 140$.<br /><br />4. Combine Like Terms<br /> Combine like terms: $11x - 3 = 140$.<br /><br />5. Solve for x<br /> Add 3 to both sides: $11x = 143$. Then divide by 11: $x = \frac{143}{11}$.<br /><br />6. Verify Solution<br /> Substitute $x = \frac{143}{11}$ back into the original equation to verify: $\frac{1}{4}(3(\frac{143}{11})+5)-\frac{1}{5}(\frac{143}{11}+7)=7$. Simplifying confirms the solution is correct.
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