Solve the Inequality for x 3 1/2>=1.4x

$3 \frac{1}{2} \geq 1.4 x$

Step 1

Simplify the left side.

Convert $3 \frac{1}{2}$ to an improper fraction.

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

$3 + \frac{1}{2} \geq 1.4 x$

Add $3$ and $\frac{1}{2}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 \cdot \frac{2}{2} + \frac{1}{2} \geq 1.4 x$

Combine $3$ and $\frac{2}{2}$ .

$\frac{3 \cdot 2}{2} + \frac{1}{2} \geq 1.4 x$

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 1}{2} \geq 1.4 x$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 + 1}{2} \geq 1.4 x$

Add $6$ and $1$ .

$\frac{7}{2} \geq 1.4 x$

Step 2

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

$1.4 x \leq \frac{7}{2}$

Step 3

Divide each term in $1.4 x \leq \frac{7}{2}$ by $1.4$ and simplify.

Divide each term in $1.4 x \leq \frac{7}{2}$ by $1.4$ .

$\frac{1.4 x}{1.4} \leq \frac{\frac{7}{2}}{1.4}$

Simplify the left side.

Cancel the common factor of $1.4$ .

Cancel the common factor.

$\frac{1.4 x}{1.4} \leq \frac{\frac{7}{2}}{1.4}$

Divide $x$ by $1$ .

$x \leq \frac{\frac{7}{2}}{1.4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \leq \frac{7}{2} \cdot \frac{1}{1.4}$

Cancel the common factor of $1.4$ .

Factor $1.4$ out of $7$ .

$x \leq \frac{1.4 (5)}{2} \cdot \frac{1}{1.4}$

Cancel the common factor.

$x \leq \frac{1.4 \cdot 5}{2} \cdot \frac{1}{1.4}$

Rewrite the expression.

$x \leq \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{5}{2}$

Interval Notation:

$(- \infty, \frac{5}{2}]$

Step 5

Solve the Inequality for x 3 1/2>=1.4x

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