Solve (y)/(6)-(3y-20)/(9) < -(2)/(3)(y-7) | 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

$$\frac{ y }{ 6 } - \frac{ 3y-20 }{ 9 } < - \frac{ 2 }{ 3 } (y-7)$$

Solve for y

$y<\frac{44}{9}$

Solution Steps

Multiply both sides of the equation by $18$, the least common multiple of $6,9,3$. Since $18$ is positive, the inequality direction remains the same.

$$3y-2\left(3y-20\right)<-12\left(y-7\right)$$

Use the distributive property to multiply $-2$ by $3y-20$.

$$3y-6y+40<-12\left(y-7\right)$$

Combine $3y$ and $-6y$ to get $-3y$.

$$-3y+40<-12\left(y-7\right)$$

Use the distributive property to multiply $-12$ by $y-7$.

$$-3y+40<-12y+84$$

Add $12y$ to both sides.

$$-3y+40+12y<84$$

Combine $-3y$ and $12y$ to get $9y$.

$$9y+40<84$$

Subtract $40$ from both sides.

$$9y<84-40$$

Subtract $40$ from $84$ to get $44$.

$$9y<44$$

Divide both sides by $9$. Since $9$ is positive, the inequality direction remains the same.

$$y<\frac{44}{9}$$