Solve for x 5 1/2>=1.6x

$5 \frac{1}{2} \geq 1.6 x$

Step 1

Simplify the left side.

Convert $5 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$5 + \frac{1}{2} \geq 1.6 x$

Add $5$ and $\frac{1}{2}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 \cdot \frac{2}{2} + \frac{1}{2} \geq 1.6 x$

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

$\frac{5 \cdot 2}{2} + \frac{1}{2} \geq 1.6 x$

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 + 1}{2} \geq 1.6 x$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 + 1}{2} \geq 1.6 x$

Add $10$ and $1$ .

$\frac{11}{2} \geq 1.6 x$

Step 2

Rewrite so $x$ is on the left side of the inequality.

$1.6 x \leq \frac{11}{2}$

Step 3

Divide each term in $1.6 x \leq \frac{11}{2}$ by $1.6$ and simplify.

Divide each term in $1.6 x \leq \frac{11}{2}$ by $1.6$ .

$\frac{1.6 x}{1.6} \leq \frac{\frac{11}{2}}{1.6}$

Simplify the left side.

Cancel the common factor of $1.6$ .

Cancel the common factor.

$\frac{1.6 x}{1.6} \leq \frac{\frac{11}{2}}{1.6}$

Divide $x$ by $1$ .

$x \leq \frac{\frac{11}{2}}{1.6}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \leq \frac{11}{2} \cdot \frac{1}{1.6}$

Divide $1$ by $1.6$ .

$x \leq \frac{11}{2} \cdot 0.625$

Multiply $\frac{11}{2} \cdot 0.625$ .

Combine $\frac{11}{2}$ and $0.625$ .

$x \leq \frac{11 \cdot 0.625}{2}$

Multiply $11$ by $0.625$ .

$x \leq \frac{6.875}{2}$

Divide $6.875$ by $2$ .

$x \leq 3.4375$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3.4375$

Interval Notation:

$(- \infty, 3.4375]$

Step 5

Solve for x 5 1/2>=1.6x

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