Algebra Examples

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

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

${(4 x - 3)}^{\frac{1}{2}}, 1$

Step 1.2

The LCM of one and any expression is the expression.

${(4 x - 3)}^{\frac{1}{2}}$

Step 2

Multiply each term in $\frac{2}{{(4 x - 3)}^{\frac{1}{2}}} = 1$ by ${(4 x - 3)}^{\frac{1}{2}}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2}{{(4 x - 3)}^{\frac{1}{2}}} = 1$ by ${(4 x - 3)}^{\frac{1}{2}}$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of ${(4 x - 3)}^{\frac{1}{2}}$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply ${(4 x - 3)}^{\frac{1}{2}}$ by $1$ .

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

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as ${(4 x - 3)}^{\frac{1}{2}} = 2$ .

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

Step 3.2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 3.3

Simplify the exponent.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify ${({(4 x - 3)}^{\frac{1}{2}})}^{2}$ .

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Step 3.3.1.1.1

Multiply the exponents in ${({(4 x - 3)}^{\frac{1}{2}})}^{2}$ .

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Step 3.3.1.1.1.1

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

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

Step 3.3.1.1.1.2

Cancel the common factor of $2$ .

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Step 3.3.1.1.1.2.1

Cancel the common factor.

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

Step 3.3.1.1.1.2.2

Rewrite the expression.

${(4 x - 3)}^{1} = 2^{2}$

Step 3.3.1.1.2

Simplify.

$4 x - 3 = 2^{2}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

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

$4 x - 3 = 4$

Step 3.4

Solve for $x$ .

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Step 3.4.1

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

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Step 3.4.1.1

Add $3$ to both sides of the equation.

$4 x = 4 + 3$

Step 3.4.1.2

Add $4$ and $3$ .

$4 x = 7$

Step 3.4.2

Divide each term in $4 x = 7$ by $4$ and simplify.

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Step 3.4.2.1

Divide each term in $4 x = 7$ by $4$ .

$\frac{4 x}{4} = \frac{7}{4}$

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Cancel the common factor of $4$ .

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Step 3.4.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{7}{4}$

Step 3.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{4}$

Decimal Form:

$x = 1.75$

Mixed Number Form:

$x = 1 \frac{3}{4}$