Questions: Solve and check the linear equation. 4y-3=10y+21 The solution set is . (Simplify your answer.)

Solve and check the linear equation. 4y-3=10y+21 The solution set is . (Simplify your answer.)
Transcript text: Solve and check the linear equation. \[ 4 y-3=10 y+21 \] The solution set is $\{$ $\square$ \}. (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Simplify the Equation

Start with the given linear equation:

\[ 4y - 3 = 10y + 21 \]

Subtract \(4y\) from both sides to get:

\[ -3 = 6y + 21 \]

Step 2: Isolate the Variable Term

Subtract 21 from both sides to isolate the term with \(y\):

\[ -3 - 21 = 6y \]

Simplify the left side:

\[ -24 = 6y \]

Step 3: Solve for \(y\)

Divide both sides by 6 to solve for \(y\):

\[ y = \frac{-24}{6} \]

Simplify the fraction:

\[ y = -4 \]

Step 4: Check the Solution

Substitute \(y = -4\) back into the original equation to verify:

\[ 4(-4) - 3 = 10(-4) + 21 \]

Calculate both sides:

\[ -16 - 3 = -40 + 21 \]

\[ -19 = -19 \]

Both sides are equal, confirming that the solution is correct.

Final Answer

The solution set is \(\boxed{-4}\).

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