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Solve for x. (2x+5)/(8)+(2x+1)/(24)=7 Answer:

Solve for x \mathrm{x} .\newline2x+58+2x+124=7 \frac{2 x+5}{8}+\frac{2 x+1}{24}=7 \newlineAnswer:

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Full solution

Q. Solve for x \mathrm{x} .\newline2x+58+2x+124=7 \frac{2 x+5}{8}+\frac{2 x+1}{24}=7 \newlineAnswer:
  1. Find Common Denominator: Find a common denominator for the fractions on the left side of the equation.\newlineThe common denominator for 88 and 2424 is 2424. We will convert the first fraction to have a denominator of 2424 by multiplying both the numerator and the denominator by 33.
  2. Rewrite with Common Denominator: Rewrite the equation with the common denominator.\newline(3(2x+5))/24+(2x+1)/24=7(3(2x+5))/24 + (2x+1)/24 = 7\newlineNow, combine the fractions.\newline(3(2x+5)+(2x+1))/24=7(3(2x+5) + (2x+1))/24 = 7
  3. Combine Fractions: Multiply both sides of the equation by 2424 to eliminate the denominator.\newline24×(3(2x+5)+(2x+1)24)=7×2424 \times \left(\frac{3(2x+5) + (2x+1)}{24}\right) = 7 \times 24\newlineThis simplifies to:\newline3(2x+5)+(2x+1)=1683(2x+5) + (2x+1) = 168
  4. Eliminate Denominator: Distribute the 33 into the first parenthesis and simplify the equation.6x+15+2x+1=1686x + 15 + 2x + 1 = 168Combine like terms.8x+16=1688x + 16 = 168
  5. Simplify Equation: Subtract 1616 from both sides of the equation to isolate the term with xx.\newline8x+16−16=168−168x + 16 - 16 = 168 - 16\newlineThis simplifies to:\newline8x=1528x = 152
  6. Isolate x Term: Divide both sides of the equation by 88 to solve for xx.\newline8x8=1528\frac{8x}{8} = \frac{152}{8}\newlineThis simplifies to:\newlinex=19x = 19

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