What's the Letters number

Question

5(a-2)=2+3a
-8(-5r+7)=7(7r+1)
x-29=-3(3+x)

Answer 1

Let's solve each equation step by step to find the values of $a$, $r$, and $x$.

Equation 1: $5(a-2)=2+3a$

1. Distribute the 5: $$5a-10=2+3a$$

2. Subtract $3a$ from both sides: $$5a-3a-10=2$$ $$2a-10=2$$

3. Add 10 to both sides: $$2a=12$$

4. Divide by 2: $$a=6$$

Equation 2: $-8(-5r+7)=7(7r+1)$

1. Distribute the -8: $$40r-56=49r+7$$

2. Subtract $40r$ from both sides: $$-56=9r+7$$

3. Subtract 7 from both sides: $$-56-7=9r$$ $$-63=9r$$

4. Divide by 9: $$r=-7$$

Equation 3: $x-29=-3(3+x)$

1. Distribute the -3: $$x-29=-9-3x$$

2. Add $3x$ to both sides: $$x+3x-29=-9$$ $$4x-29=-9$$

3. Add 29 to both sides: $$4x=20$$

4. Divide by 4: $$x=5$$

Summary of Solutions

• $a=6$
• $r=-7$
• $x=5$

Let me know if you need further assistance!