Solve for x 1/2(5x+1)^(1/3)+5/2=4

$\frac{1}{2} {(5 x + 1)}^{\frac{1}{3}} + \frac{5}{2} = 4$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $\frac{5}{2}$ from both sides of the equation.

$\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}} = 4 - \frac{5}{2}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}} = 4 \cdot \frac{2}{2} - \frac{5}{2}$

Combine $4$ and $\frac{2}{2}$ .

$\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}} = \frac{4 \cdot 2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}} = \frac{4 \cdot 2 - 5}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}} = \frac{8 - 5}{2}$

Subtract $5$ from $8$ .

$\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}} = \frac{3}{2}$

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}})}^{3} = {(\frac{3}{2})}^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${(\frac{1}{2} \cdot {(5 x + 1)}^{\frac{1}{3}})}^{3}$ .

Combine fractions.

Combine $\frac{1}{2}$ and ${(5 x + 1)}^{\frac{1}{3}}$ .

${(\frac{{(5 x + 1)}^{\frac{1}{3}}}{2})}^{3} = {(\frac{3}{2})}^{3}$

Apply the product rule to $\frac{{(5 x + 1)}^{\frac{1}{3}}}{2}$ .

$\frac{{({(5 x + 1)}^{\frac{1}{3}})}^{3}}{2^{3}} = {(\frac{3}{2})}^{3}$

Simplify the numerator.

Multiply the exponents in ${({(5 x + 1)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{{(5 x + 1)}^{\frac{1}{3} \cdot 3}}{2^{3}} = {(\frac{3}{2})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{{(5 x + 1)}^{\frac{1}{3} \cdot 3}}{2^{3}} = {(\frac{3}{2})}^{3}$

Rewrite the expression.

$\frac{{(5 x + 1)}^{1}}{2^{3}} = {(\frac{3}{2})}^{3}$

Simplify.

$\frac{5 x + 1}{2^{3}} = {(\frac{3}{2})}^{3}$

Raise $2$ to the power of $3$ .

$\frac{5 x + 1}{8} = {(\frac{3}{2})}^{3}$

Split the fraction $\frac{5 x + 1}{8}$ into two fractions.

$\frac{5 x}{8} + \frac{1}{8} = {(\frac{3}{2})}^{3}$

Simplify the right side.

Simplify ${(\frac{3}{2})}^{3}$ .

Apply the product rule to $\frac{3}{2}$ .

$\frac{5 x}{8} + \frac{1}{8} = \frac{3^{3}}{2^{3}}$

Raise $3$ to the power of $3$ .

$\frac{5 x}{8} + \frac{1}{8} = \frac{27}{2^{3}}$

Raise $2$ to the power of $3$ .

$\frac{5 x}{8} + \frac{1}{8} = \frac{27}{8}$

Step 4

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $\frac{1}{8}$ from both sides of the equation.

$\frac{5 x}{8} = \frac{27}{8} - \frac{1}{8}$

Combine the numerators over the common denominator.

$\frac{5 x}{8} = \frac{27 - 1}{8}$

Subtract $1$ from $27$ .

$\frac{5 x}{8} = \frac{26}{8}$

Cancel the common factor of $26$ and $8$ .

Factor $2$ out of $26$ .

$\frac{5 x}{8} = \frac{2 (13)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{5 x}{8} = \frac{2 \cdot 13}{2 \cdot 4}$

Cancel the common factor.

$\frac{5 x}{8} = \frac{2 \cdot 13}{2 \cdot 4}$

Rewrite the expression.

$\frac{5 x}{8} = \frac{13}{4}$

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} \cdot \frac{5 x}{8} = \frac{8}{5} \cdot \frac{13}{4}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{5} \cdot \frac{5 x}{8}$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 x}{8} = \frac{8}{5} \cdot \frac{13}{4}$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{8}{5} \cdot \frac{13}{4}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{8}{5} \cdot \frac{13}{4}$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{8}{5} \cdot \frac{13}{4}$

Rewrite the expression.

$x = \frac{8}{5} \cdot \frac{13}{4}$

Simplify the right side.

Simplify $\frac{8}{5} \cdot \frac{13}{4}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x = \frac{4 (2)}{5} \cdot \frac{13}{4}$

Cancel the common factor.

$x = \frac{4 \cdot 2}{5} \cdot \frac{13}{4}$

Rewrite the expression.

$x = \frac{2}{5} \cdot 13$

Combine $\frac{2}{5}$ and $13$ .

$x = \frac{2 \cdot 13}{5}$

Multiply $2$ by $13$ .

$x = \frac{26}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{26}{5}$

Decimal Form:

$x = 5.2$

Mixed Number Form:

$x = 5 \frac{1}{5}$

Solve for x 1/2(5x+1)^(1/3)+5/2=4

Related Questions

Support LCMGCF.com by disabling your adblocker.