Question

1. solve and check

$1 + 2r = 35$
answer:

1. solve and check

$42 + 5t = 8t$
answer:

Explanation:

For problem 6: $1 + 2r = 35$

Step1: Isolate the term with $r$

Subtract 1 from both sides:
$1 + 2r - 1 = 35 - 1$
$2r = 34$

Step2: Solve for $r$

Divide both sides by 2:
$\frac{2r}{2} = \frac{34}{2}$
$r = 17$

Step3: Verify the solution

Substitute $r=17$ into original equation:
$1 + 2(17) = 1 + 34 = 35$, which matches the right-hand side.

For problem 8: $42 + 5t = 8t$

Step1: Isolate terms with $t$

Subtract $5t$ from both sides:
$42 + 5t - 5t = 8t - 5t$
$42 = 3t$

Step2: Solve for $t$

Divide both sides by 3:
$\frac{42}{3} = \frac{3t}{3}$
$t = 14$

Step3: Verify the solution

Substitute $t=14$ into original equation:
$42 + 5(14) = 42 + 70 = 112$, and $8(14)=112$, both sides are equal.

Answer:

For problem 6: $r = 17$
For problem 8: $t = 14$