Question 541·Easy·Algebra

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If $\tfrac{3}{2}t + 7 = 31$ what is the value of $t$ ?

Your answer

In a linear equation, the unknown appears only to the first power. Here, a fraction multiplies the unknown, and then a number is added. Undo the addition before undoing the multiplication. Desmos can solve the equation with a regression, but don’t mistake the value of the term containing the unknown for the value of the unknown itself.

Hints

Hint 1
The $+7$ comes after the multiplication. Subtract $7$ from both sides to leave the term containing $t$ alone. What value does that whole term equal?
Hint 2
A regression uses $\sim$ to find an unknown. Replace the equation’s $=$ with $\sim$ in Desmos, then read the value of $t$ under PARAMETERS.

Step-by-step

Approach 1: Subtract, then solve in Desmos
Step 1
Remove the added number
The $7$ is added to $\frac32t$ , so subtract $7$ from both sides to keep them equal:
$\frac32t=31-7=24.$
Step 2
Find the value of t
Type the original equation in Desmos with $\sim$ in place of $=$ : $\frac32t+7\sim31$ . The $\sim$ tells Desmos to solve for $t$ ; under PARAMETERS, it shows $t=16$ . The question asks for $t$ , not the intermediate value $24$ , so Grid in 16.

Approach 2: Undo the fraction by hand
Step 1
Cancel the coefficient
From $\frac32t=24$ , multiply both sides by $\frac23$ , the reciprocal of $\frac32$ . These fractions multiply to $1$ , leaving $t$ alone:
$t=24\times\frac23.$
Step 2
Calculate t
Multiply: $t=16$ . So the value of $t$ is $16$ . Grid in 16.

Question 541·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this