Solved on Jan 18, 2024

Solve the cubic equation $\sqrt[3]{5x-3}-2=0$ for $x$ .

STEP 1

Assumptions
1. We are given the equation $\sqrt[3]{5x - 3} - 2 = 0$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to isolate the cube root term on one side of the equation. We can do this by adding $2$ to both sides of the equation.
$\sqrt[3]{5x - 3} - 2 + 2 = 0 + 2$

STEP 3

Simplify both sides of the equation.
$\sqrt[3]{5x - 3} = 2$

STEP 4

Now, to eliminate the cube root, we can raise both sides of the equation to the power of $3$ .
$(\sqrt[3]{5x - 3})^3 = 2^3$

STEP 5

Calculate the cube of $2$ .
$2^3 = 8$

STEP 6

The cube of a cube root will cancel out, leaving us with the expression inside the cube root.
$(5x - 3) = 8$

STEP 7

Next, we need to solve for $x$ by isolating it. We can do this by adding $3$ to both sides of the equation.
$5x - 3 + 3 = 8 + 3$

STEP 8

Simplify both sides of the equation.
$5x = 11$

STEP 9

Now, we need to divide both sides of the equation by $5$ to solve for $x$ .
$\frac{5x}{5} = \frac{11}{5}$

STEP 10

Simplify both sides of the equation to find the value of $x$ .
$x = \frac{11}{5}$
$x = \frac{11}{5}$ is the solution to the equation $\sqrt[3]{5x - 3} - 2 = 0$ .

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Solve the cubic equation $\sqrt[3]{5x-3}-2=0$ for $x$ .

STEP 1

Assumptions
1. We are given the equation $\sqrt[3]{5x - 3} - 2 = 0$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to isolate the cube root term on one side of the equation. We can do this by adding $2$ to both sides of the equation.
$\sqrt[3]{5x - 3} - 2 + 2 = 0 + 2$

STEP 3

Simplify both sides of the equation.
$\sqrt[3]{5x - 3} = 2$

STEP 4

Now, to eliminate the cube root, we can raise both sides of the equation to the power of $3$ .
$(\sqrt[3]{5x - 3})^3 = 2^3$

STEP 5

Calculate the cube of $2$ .
$2^3 = 8$

STEP 6

The cube of a cube root will cancel out, leaving us with the expression inside the cube root.
$(5x - 3) = 8$

STEP 7

Next, we need to solve for $x$ by isolating it. We can do this by adding $3$ to both sides of the equation.
$5x - 3 + 3 = 8 + 3$

STEP 8

Simplify both sides of the equation.
$5x = 11$

STEP 9

Now, we need to divide both sides of the equation by $5$ to solve for $x$ .
$\frac{5x}{5} = \frac{11}{5}$

STEP 10

Simplify both sides of the equation to find the value of $x$ .
$x = \frac{11}{5}$
$x = \frac{11}{5}$ is the solution to the equation $\sqrt[3]{5x - 3} - 2 = 0$ .

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Solve the cubic equation 5x−33−2=0\sqrt[3]{5x-3}-2=035x−3​−2=0 for xxx.

STEP 1

Assumptions1. We are given the equation 5x−33−2=0\sqrt[3]{5x - 3} - 2 = 035x−3​−2=0.2. We need to solve for the variable xxx.

STEP 2

First, we need to isolate the cube root term on one side of the equation. We can do this by adding 222 to both sides of the equation.5x−33−2+2=0+2\sqrt[3]{5x - 3} - 2 + 2 = 0 + 235x−3​−2+2=0+2

STEP 3

Simplify both sides of the equation.5x−33=2\sqrt[3]{5x - 3} = 235x−3​=2

STEP 4

Now, to eliminate the cube root, we can raise both sides of the equation to the power of 333.(5x−33)3=23(\sqrt[3]{5x - 3})^3 = 2^3(35x−3​)3=23

STEP 5

Calculate the cube of 222.23=82^3 = 823=8

STEP 6

The cube of a cube root will cancel out, leaving us with the expression inside the cube root.(5x−3)=8(5x - 3) = 8(5x−3)=8

STEP 7

Next, we need to solve for xxx by isolating it. We can do this by adding 333 to both sides of the equation.5x−3+3=8+35x - 3 + 3 = 8 + 35x−3+3=8+3

STEP 8

Simplify both sides of the equation.5x=115x = 115x=11

STEP 9

Now, we need to divide both sides of the equation by 555 to solve for xxx.5x5=115\frac{5x}{5} = \frac{11}{5}55x​=511​

STEP 10

Simplify both sides of the equation to find the value of xxx.x=115x = \frac{11}{5}x=511​x=115x = \frac{11}{5}x=511​ is the solution to the equation 5x−33−2=0\sqrt[3]{5x - 3} - 2 = 035x−3​−2=0.

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Solve the cubic equation $\sqrt[3]{5x-3}-2=0$ for $x$ .

Assumptions
1. We are given the equation $\sqrt[3]{5x - 3} - 2 = 0$ .
2. We need to solve for the variable $x$ .

First, we need to isolate the cube root term on one side of the equation. We can do this by adding $2$ to both sides of the equation.
$\sqrt[3]{5x - 3} - 2 + 2 = 0 + 2$

Simplify both sides of the equation.
$\sqrt[3]{5x - 3} = 2$

Now, to eliminate the cube root, we can raise both sides of the equation to the power of $3$ .
$(\sqrt[3]{5x - 3})^3 = 2^3$

Calculate the cube of $2$ .
$2^3 = 8$

The cube of a cube root will cancel out, leaving us with the expression inside the cube root.
$(5x - 3) = 8$

Next, we need to solve for $x$ by isolating it. We can do this by adding $3$ to both sides of the equation.
$5x - 3 + 3 = 8 + 3$

Simplify both sides of the equation.
$5x = 11$

Now, we need to divide both sides of the equation by $5$ to solve for $x$ .
$\frac{5x}{5} = \frac{11}{5}$

Simplify both sides of the equation to find the value of $x$ .
$x = \frac{11}{5}$
$x = \frac{11}{5}$ is the solution to the equation $\sqrt[3]{5x - 3} - 2 = 0$ .