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

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. The common denominator for 8 and 24 is 24. We will convert the first fraction to have a denominator of 24 by multiplying both the numerator and the denominator by 3.Rewrite with Common Denominator: Rewrite the equation with the common denominator. (3*(2x+5))/24 + (2x+1)/24 = 7 Now, combine the fractions. (3*(2x+5) + (2x+1))/24 = 7Combine Fractions: Multiply both sides of the equation by 24 to eliminate the denominator. 24 * ((3*(2x+5) + (2x+1))/24) = 7 * 24 This simplifies to: 3*(2x+5) + (2x+1) = 168Eliminate Denominator: Distribute the 3 into the first parenthesis and simplify the equation. 6x + 15 + 2x + 1 = 168 Combine like terms. 8x + 16 = 168Simplify Equation: Subtract 16 from both sides of the equation to isolate the term with x. 8x + 16 - 16 = 168 - 16 This simplifies to: 8x = 152Isolate x Term: Divide both sides of the equation by 8 to solve for x. 8x / 8 = 152 / 8 This simplifies to: x = 19

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for
x.

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

Solve for $\mathrm{x}$ . $\newline$ $\frac{2 x+5}{8}+\frac{2 x+1}{24}=7$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 6

Factor numerical expressions using the distributive property

Full solution

Q. Solve for

\mathrm{x}

\newline

\frac{2 x+5}{8}+\frac{2 x+1}{24}=7

\newline

Answer:

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. $\newline$ The common denominator for $8$ and $24$ is $24$ . We will convert the first fraction to have a denominator of $24$ by multiplying both the numerator and the denominator by $3$ .
Rewrite with Common Denominator: Rewrite the equation with the common denominator. $\newline$ $(3(2x+5))/24 + (2x+1)/24 = 7$ $\newline$ Now, combine the fractions. $\newline$ $(3(2x+5) + (2x+1))/24 = 7$
Combine Fractions: Multiply both sides of the equation by $24$ to eliminate the denominator. $\newline$ $24 \times \left(\frac{3(2x+5) + (2x+1)}{24}\right) = 7 \times 24$ $\newline$ This simplifies to: $\newline$ $3(2x+5) + (2x+1) = 168$
Eliminate Denominator: Distribute the $3$ into the first parenthesis and simplify the equation. $6x + 15 + 2x + 1 = 168$ Combine like terms. $8x + 16 = 168$
Simplify Equation: Subtract $16$ from both sides of the equation to isolate the term with $x$ . $\newline$ $8x + 16 - 16 = 168 - 16$ $\newline$ This simplifies to: $\newline$ $8x = 152$
Isolate x Term: Divide both sides of the equation by $8$ to solve for $x$ . $\newline$ $\frac{8x}{8} = \frac{152}{8}$ $\newline$ This simplifies to: $\newline$ $x = 19$