Algebra Examples

$5 (7 - x) + 2 x < 6 x - 2 - 9 x$

Step 1

Simplify $5 (7 - x) + 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 \cdot 7 + 5 (- x) + 2 x < 6 x - 2 - 9 x$

Step 1.1.2

Multiply $5$ by $7$ .

$35 + 5 (- x) + 2 x < 6 x - 2 - 9 x$

Step 1.1.3

Multiply $- 1$ by $5$ .

$35 - 5 x + 2 x < 6 x - 2 - 9 x$

$35 - 5 x + 2 x < 6 x - 2 - 9 x$

Step 1.2

Add $- 5 x$ and $2 x$ .

$35 - 3 x < 6 x - 2 - 9 x$

$35 - 3 x < 6 x - 2 - 9 x$

Step 2

Subtract $9 x$ from $6 x$ .

$35 - 3 x < - 3 x - 2$

Step 3

Move all terms containing $x$ to the left side of the inequality.

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Step 3.1

Add $3 x$ to both sides of the inequality.

$35 - 3 x + 3 x < - 2$

Step 3.2

Combine the opposite terms in $35 - 3 x + 3 x$ .

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Step 3.2.1

Add $- 3 x$ and $3 x$ .

$35 + 0 < - 2$

Step 3.2.2

Add $35$ and $0$ .

$35 < - 2$

$35 < - 2$

$35 < - 2$

Step 4

Since $35 > - 2$ , there are no solutions.

No solution

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$