To remove the radical on the left side of the inequality, square both sides of the inequality.

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mi>x</mi><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>5</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mn>5</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Simplify the right side.

Raise <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the inequality.

Add <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> to both sides of the inequality.

Add <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>25</mn><mi>x</mi><mo>></mo><mn>125</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>25</mn><mi>x</mi><mo>></mo><mn>125</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>125</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Set the radicand in <math><mstyle displaystyle="true"><msqrt><mi>x</mi><mo>-</mo><mn>1</mn></msqrt></mstyle></math> greater than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to find where the expression is defined.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the inequality.

The domain is all values of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> that make the expression defined.

The solution consists of all of the true intervals.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Do you know how to Solve the Inequality for x 5 square root of x-1>10? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | three hundred million four hundred seventy-nine thousand four hundred thirty-nine |
---|

- 300479439 has 16 divisors, whose sum is
**431877600** - The reverse of 300479439 is
**934974003** - Previous prime number is
**1229**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 39
- Digital Root 3

Name | one billion one hundred ninety-seven million four hundred fifty thousand one hundred twenty-two |
---|

- 1197450122 has 64 divisors, whose sum is
**2348352000** - The reverse of 1197450122 is
**2210547911** - Previous prime number is
**149**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 32
- Digital Root 5

Name | one billion seven hundred eighteen million five hundred thirty-five thousand five hundred eighteen |
---|

- 1718535518 has 8 divisors, whose sum is
**2946060912** - The reverse of 1718535518 is
**8155358171** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 44
- Digital Root 8