Solve (320^2-160^2)*1/160geq11/4

$$( 320 ^ { 2 } - 160 ^ { 2 } ) \times \frac { 1 } { 160 } \geq 1 \frac { 1 } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 160, the least common multiple of 160,4. Since 160 is positive, the inequality direction remains the same.

$$160\left(320^{2}-160^{2}\right)\times \frac{1}{160}\geq 40\left(1\times 4+1\right)$$

Calculate 320 to the power of 2 and get 102400.

$$160\left(102400-160^{2}\right)\times \frac{1}{160}\geq 40\left(1\times 4+1\right)$$

Calculate 160 to the power of 2 and get 25600.

$$160\left(102400-25600\right)\times \frac{1}{160}\geq 40\left(1\times 4+1\right)$$

Subtract 25600 from 102400 to get 76800.

$$160\times 76800\times \frac{1}{160}\geq 40\left(1\times 4+1\right)$$

Multiply 160 and 76800 to get 12288000.

$$12288000\times \frac{1}{160}\geq 40\left(1\times 4+1\right)$$

Multiply 12288000 and \frac{1}{160} to get \frac{12288000}{160}.

$$\frac{12288000}{160}\geq 40\left(1\times 4+1\right)$$

Divide 12288000 by 160 to get 76800.

$$76800\geq 40\left(1\times 4+1\right)$$

Multiply 1 and 4 to get 4.

$$76800\geq 40\left(4+1\right)$$

Add 4 and 1 to get 5.

$$76800\geq 40\times 5$$

Multiply 40 and 5 to get 200.

$$76800\geq 200$$

Compare 76800 and 200.

$$\text{true}$$