Math / Algebra

QuestionSolve. $\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}$

Studdy Solution

STEP 1

1. The equation $5.4 = -\frac{t}{7.5}$ is asking us to solve for $t$ .
2. This is a one-step equation involving division.
3. The equation involves basic algebraic operations, specifically multiplication to isolate $t$ .

STEP 2

1. Understand the structure of the equation.
2. Isolate the variable $t$ by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.

STEP 3

The equation $5.4 = -\frac{t}{7.5}$ implies that $t$ is divided by $7.5$ and then multiplied by $-1$ to give $5.4$ .

STEP 4

To isolate $t$ , we need to perform the inverse operation of division by $7.5$ . Multiply both sides of the equation by $-7.5$ :
$5.4 \times (-7.5) = -\frac{t}{7.5} \times (-7.5)$

STEP 5

Simplify both sides of the equation:
$-40.5 = t$

STEP 6

Verify the solution by substituting $t = -40.5$ back into the original equation:
$5.4 = -\frac{-40.5}{7.5}$

STEP 7

Simplify the right-hand side:
$5.4 = \frac{40.5}{7.5}$
Calculate the division:
$5.4 = 5.4$
Both sides are equal, confirming our solution is correct.
The solution is:
$\boxed{-40.5}$

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QuestionSolve. $\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}$

Studdy Solution

STEP 1

1. The equation $5.4 = -\frac{t}{7.5}$ is asking us to solve for $t$ .
2. This is a one-step equation involving division.
3. The equation involves basic algebraic operations, specifically multiplication to isolate $t$ .

STEP 2

1. Understand the structure of the equation.
2. Isolate the variable $t$ by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.

STEP 3

The equation $5.4 = -\frac{t}{7.5}$ implies that $t$ is divided by $7.5$ and then multiplied by $-1$ to give $5.4$ .

STEP 4

To isolate $t$ , we need to perform the inverse operation of division by $7.5$ . Multiply both sides of the equation by $-7.5$ :
$5.4 \times (-7.5) = -\frac{t}{7.5} \times (-7.5)$

STEP 5

Simplify both sides of the equation:
$-40.5 = t$

STEP 6

Verify the solution by substituting $t = -40.5$ back into the original equation:
$5.4 = -\frac{-40.5}{7.5}$

STEP 7

Simplify the right-hand side:
$5.4 = \frac{40.5}{7.5}$
Calculate the division:
$5.4 = 5.4$
Both sides are equal, confirming our solution is correct.
The solution is:
$\boxed{-40.5}$

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QuestionSolve. 5.4=−t7.5t=\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}5.4t​=−7.5t​=​

Studdy Solution

STEP 1

1. The equation 5.4=−t7.5 5.4 = -\frac{t}{7.5} 5.4=−7.5t​ is asking us to solve for t t t.2. This is a one-step equation involving division.3. The equation involves basic algebraic operations, specifically multiplication to isolate t t t.

STEP 2

1. Understand the structure of the equation.2. Isolate the variable t t t by performing algebraic operations.3. Verify the solution by substituting it back into the original equation.

STEP 3

The equation 5.4=−t7.5 5.4 = -\frac{t}{7.5} 5.4=−7.5t​ implies that t t t is divided by 7.5 7.5 7.5 and then multiplied by −1-1−1 to give 5.4 5.4 5.4.

STEP 4

To isolate t t t, we need to perform the inverse operation of division by 7.5 7.5 7.5. Multiply both sides of the equation by −7.5-7.5−7.5:5.4×(−7.5)=−t7.5×(−7.5) 5.4 \times (-7.5) = -\frac{t}{7.5} \times (-7.5) 5.4×(−7.5)=−7.5t​×(−7.5)

STEP 5

Simplify both sides of the equation:−40.5=t -40.5 = t −40.5=t

STEP 6

Verify the solution by substituting t=−40.5 t = -40.5 t=−40.5 back into the original equation:5.4=−−40.57.5 5.4 = -\frac{-40.5}{7.5} 5.4=−7.5−40.5​

STEP 7

Simplify the right-hand side:5.4=40.57.5 5.4 = \frac{40.5}{7.5} 5.4=7.540.5​Calculate the division:5.4=5.4 5.4 = 5.4 5.4=5.4Both sides are equal, confirming our solution is correct. The solution is:−40.5 \boxed{-40.5} −40.5​

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QuestionSolve. $\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}$

1. The equation $5.4 = -\frac{t}{7.5}$ is asking us to solve for $t$ .
2. This is a one-step equation involving division.
3. The equation involves basic algebraic operations, specifically multiplication to isolate $t$ .

1. Understand the structure of the equation.
2. Isolate the variable $t$ by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.

The equation $5.4 = -\frac{t}{7.5}$ implies that $t$ is divided by $7.5$ and then multiplied by $-1$ to give $5.4$ .

To isolate $t$ , we need to perform the inverse operation of division by $7.5$ . Multiply both sides of the equation by $-7.5$ :
$5.4 \times (-7.5) = -\frac{t}{7.5} \times (-7.5)$

Simplify both sides of the equation:
$-40.5 = t$

Verify the solution by substituting $t = -40.5$ back into the original equation:
$5.4 = -\frac{-40.5}{7.5}$

Simplify the right-hand side:
$5.4 = \frac{40.5}{7.5}$
Calculate the division:
$5.4 = 5.4$
Both sides are equal, confirming our solution is correct.
The solution is:
$\boxed{-40.5}$