Solve for x in simplest form. 2=(3)/(4)(3x+16) Answer:

Write Equation: Write down the equation given by the problem. The equation is 2 = (3/4)(3x + 16).Multiply by Reciprocal: To isolate the term with x, multiply both sides of the equation by the reciprocal of (3/4), which is (4/3). Doing this, we get (4/3) * 2 = (4/3) * (3/4) * (3x + 16).Simplify Equation: Simplify both sides of the equation. On the left side, (4/3) * 2 simplifies to 8/3. On the right side, (4/3) * (3/4) simplifies to 1, leaving us with 3x + 16. So, we have 8/3 = 3x + 16.Subtract 16: Subtract 16 from both sides to isolate the term with x on one side. 8/3 - 16 = 3x + 16 - 16.Combine Left Side: Simplify the left side of the equation. To subtract 16 from 8/3, we need a common denominator. The common denominator is 3, so we convert 16 to 48/3. Now we have 8/3 - 48/3 = 3x.Divide by 3: Combine the terms on the left side. 8/3 - 48/3 simplifies to -40/3. So, we have -40/3 = 3x.Divide both sides by 3 to solve for x. -40/3 divided by 3 is -40/9. So, we have x = -40/9.

Home

Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

Q. Solve for

\mathrm{x}

in simplest form.

\newline

2=\frac{3}{4}(3 x+16)

\newline

Answer:

Write Equation: Write down the equation given by the problem. $\newline$ The equation is $2 = \left(\frac{3}{4}\right)(3x + 16)$ .
Multiply by Reciprocal: To isolate the term with $x$ , multiply both sides of the equation by the reciprocal of $\frac{3}{4}$ , which is $\frac{4}{3}$ . $\newline$ Doing this, we get $\frac{4}{3} \times 2 = \frac{4}{3} \times \frac{3}{4} \times (3x + 16)$ .
Simplify Equation: Simplify both sides of the equation. $\newline$ On the left side, $(\frac{4}{3}) \times 2$ simplifies to $\frac{8}{3}$ . $\newline$ On the right side, $(\frac{4}{3}) \times (\frac{3}{4})$ simplifies to $1$ , leaving us with $3x + 16$ . $\newline$ So, we have $\frac{8}{3} = 3x + 16$ .
Subtract $16$ : Subtract $16$ from both sides to isolate the term with $x$ on one side. $\newline$ $\frac{8}{3} - 16 = 3x + 16 - 16.$
Combine Left Side: Simplify the left side of the equation. $\newline$ To subtract $16$ from $\frac{8}{3}$ , we need a common denominator. The common denominator is $3$ , so we convert $16$ to $\frac{48}{3}$ . $\newline$ Now we have $\frac{8}{3} - \frac{48}{3} = 3x$ .
Divide by $3$ : Combine the terms on the left side. $\newline$ $\frac{8}{3} - \frac{48}{3}$ simplifies to $-\frac{40}{3}$ . $\newline$ So, we have $-\frac{40}{3} = 3x$ .
Divide by $3$ : Combine the terms on the left side. $\newline$ $\frac{8}{3} - \frac{48}{3}$ simplifies to $-\frac{40}{3}$ . $\newline$ So, we have $-\frac{40}{3} = 3x$ .Divide both sides by $3$ to solve for x. $\newline$ $-\frac{40}{3}$ divided by $3$ is $-\frac{40}{9}$ . $\newline$ So, we have $x = -\frac{40}{9}$ .