If 5x+(3)/(2)=6-(2)/(3)x, what is the value of x ? Choose 1 answer: (A) (27)/(34) (B) (27)/(26) (c) (45)/(34) (D) (51)/(2)

Write equation: Write down the given equation. We have the equation 5x + (3/2) = 6 - (2/3)x.Clear fractions: Clear the fractions by finding a common denominator for the terms with fractions. The common denominator for 2 and 3 is 6. Multiply every term in the equation by 6 to eliminate the fractions. 6 * (5x) + 6 * (3/2) = 6 * 6 - 6 * (2/3)xMultiply by common denominator: Simplify the equation by performing the multiplications. 30x + 9 = 36 - 4xSimplify equation: Move all x terms to one side of the equation and constants to the other side. Add 4x to both sides to get all x terms on one side. 30x + 4x + 9 = 36 - 4x + 4xRearrange terms: Combine like terms. 34x + 9 = 36Combine like terms: Subtract 9 from both sides to isolate the term with x. 34x + 9 - 9 = 36 - 9Isolate x term: Simplify the equation. 34x = 27Simplify equation: Divide both sides by 34 to solve for x. x = 27 / 34

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
5x+(3)/(2)=6-(2)/(3)x, what is the value of
x ?
Choose 1 answer:
(A)
(27)/(34)
(B)
(27)/(26)
(c)
(45)/(34)
(D)
(51)/(2)

If $5x+\frac{3}{2}=6-\frac{2}{3}x$ , what is the value of $x$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{27}{34}$ $\newline$ (B) $\frac{27}{26}$ $\newline$ (C) $\frac{45}{34}$ $\newline$ (D) $\frac{51}{2}$

View step-by-step help

Full solution

Q. If

5x+\frac{3}{2}=6-\frac{2}{3}x

, what is the value of

x

\newline

Choose

1

answer:

\newline

(A)

\frac{27}{34}

\newline

(B)

\frac{27}{26}

\newline

(C)

\frac{45}{34}

\newline

(D)

\frac{51}{2}

Write equation: Write down the given equation. $\newline$ We have the equation $5x + \left(\frac{3}{2}\right) = 6 - \left(\frac{2}{3}\right)x$ .
Clear fractions: Clear the fractions by finding a common denominator for the terms with fractions. $\newline$ The common denominator for $2$ and $3$ is $6$ . Multiply every term in the equation by $6$ to eliminate the fractions. $\newline$ $$6$ \times ($5$x) + $6$ \times \left(\frac{$3$}{$2$}\right) = $6$ \times $6$ - $6$ \times \left(\frac{$2$}{$3$}\right)x
Multiply by common denominator: Simplify the equation by performing the multiplications. $30x + 9 = 36 - 4x$
Simplify equation: Move all $x$ terms to one side of the equation and constants to the other side.$\newline$Add $4x$ to both sides to get all $x$ terms on one side.$\newline$$30x + 4x + 9 = 36 - 4x + 4x$
Rearrange terms: Combine like terms. $34x + 9 = 36$
Combine like terms: Subtract $9$ from both sides to isolate the term with $x$.$\newline$\[34x + 9 - 9 = 36 - 9\]
Isolate x term: Simplify the equation. $34x = 27$
Simplify equation: Divide both sides by $34$ to solve for $x$.$\newline$$x = \frac{27}{34}$