Question

name:
writing & solving equations review
write an equation for each statement:

1. the sum of a number and 9 is 20.
2. a number decreased by 4 equals twice that number.
3. the perimeter p of a rectangle is twice the sum of its length l and width w.

solve for x:

1. x - 6 = 9
2. 5x = 25
3. $\frac{x}{8}$ = 2
4. 4x + 9 = 25
5. 3(x - 2) = 12

Explanation:

Step1: Write equations for statements

1. Let the number be $x$. The sum of a number and 9 is 20, so the equation is $x + 9=20$.
2. Let the number be $x$. A number decreased by 4 equals twice that number, so the equation is $x - 4 = 2x$.
3. The perimeter $P$ of a rectangle is twice the sum of its length $l$ and width $w$, so the equation is $P = 2(l + w)$.

Step2: Solve equations for $x$

1. Given $x - 6=9$. Add 6 to both sides: $x-6 + 6=9 + 6$, so $x = 15$.
2. Given $5x = 25$. Divide both sides by 5: $\frac{5x}{5}=\frac{25}{5}$, so $x = 5$.
3. Given $\frac{x}{8}=2$. Multiply both sides by 8: $\frac{x}{8}\times8=2\times8$, so $x = 16$.
4. Given $4x + 9=25$. Subtract 9 from both sides: $4x+9 - 9=25 - 9$, then $4x = 16$. Divide both sides by 4: $\frac{4x}{4}=\frac{16}{4}$, so $x = 4$.
5. Given $3(x - 2)=12$. First, expand the left - hand side: $3x-6 = 12$. Add 6 to both sides: $3x-6 + 6=12 + 6$, then $3x = 18$. Divide both sides by 3: $\frac{3x}{3}=\frac{18}{3}$, so $x = 6$.

Answer:

1. $x + 9 = 20$
2. $x - 4 = 2x$
3. $P = 2(l + w)$
4. $x = 15$
5. $x = 5$
6. $x = 16$
7. $x = 4$
8. $x = 6$