Solve 0.5(x+3)-0.8 < 0.4(x+2)-0.3 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$0.5(x+3)-0.8 < 0.4(x+2)-0.3$$

Solve for x

$x<-2$

Solution Steps

Use the distributive property to multiply $0.5$ by $x+3$.

$$0.5x+1.5-0.8<0.4\left(x+2\right)-0.3$$

Subtract $0.8$ from $1.5$ to get $0.7$.

$$0.5x+0.7<0.4\left(x+2\right)-0.3$$

Use the distributive property to multiply $0.4$ by $x+2$.

$$0.5x+0.7<0.4x+0.8-0.3$$

Subtract $0.3$ from $0.8$ to get $0.5$.

$$0.5x+0.7<0.4x+0.5$$

Subtract $0.4x$ from both sides.

$$0.5x+0.7-0.4x<0.5$$

Combine $0.5x$ and $-0.4x$ to get $0.1x$.

$$0.1x+0.7<0.5$$

Subtract $0.7$ from both sides.

$$0.1x<0.5-0.7$$

Subtract $0.7$ from $0.5$ to get $-0.2$.

$$0.1x<-0.2$$

Divide both sides by $0.1$. Since $0.1$ is positive, the inequality direction remains the same.

$$x<\frac{-0.2}{0.1}$$

Expand $\frac{-0.2}{0.1}$ by multiplying both numerator and the denominator by $10$. Anything divided by one gives itself.

$$x<-2$$