Question

solve and check.

1. $2x - 3.6 = 4.4$
2. $5y + 1.3 = 21.3$
3. $4y - 1.3 = 8.7$
4. $3x + 2.1 = 11.7$

solve and check.

1. $4z + 12 = 7z - 9$
2. $8y + 2y = 6y + 16$
3. $10n + 12 - 9 - 7n + 4n = 31$
4. $12 + 2t + 7t + 4t = 64$

solve and check.

1. $3(x - 5) = 9$
2. $9(n + 2) = n + 26$
3. $3 + 6s = 4(s - 3) + 19$
4. $4(d - 4) + 2 = 3(d + 1)$

Explanation:

Problem 17: \(2x - 3.6 = 4.4\)

Step 1: Add 3.6 to both sides

To isolate the term with \(x\), we add 3.6 to both sides of the equation.
\(2x - 3.6 + 3.6 = 4.4 + 3.6\)
\(2x = 8\)

Step 2: Divide both sides by 2

To solve for \(x\), we divide both sides of the equation by 2.
\(\frac{2x}{2} = \frac{8}{2}\)
\(x = 4\)

Check:

Substitute \(x = 4\) back into the original equation:
Left side: \(2(4) - 3.6 = 8 - 3.6 = 4.4\)
Right side: \(4.4\)
Since left side = right side, \(x = 4\) is correct.

Step 1: Subtract 1.3 from both sides

To isolate the term with \(y\), we subtract 1.3 from both sides.
\(5y + 1.3 - 1.3 = 21.3 - 1.3\)
\(5y = 20\)

Step 2: Divide both sides by 5

To solve for \(y\), we divide both sides by 5.
\(\frac{5y}{5} = \frac{20}{5}\)
\(y = 4\)

Check:

Substitute \(y = 4\) back into the original equation:
Left side: \(5(4) + 1.3 = 20 + 1.3 = 21.3\)
Right side: \(21.3\)
Since left side = right side, \(y = 4\) is correct.

Step 1: Add 1.3 to both sides

To isolate the term with \(y\), we add 1.3 to both sides.
\(4y - 1.3 + 1.3 = 8.7 + 1.3\)
\(4y = 10\)

Step 2: Divide both sides by 4

To solve for \(y\), we divide both sides by 4.
\(\frac{4y}{4} = \frac{10}{4}\)
\(y = 2.5\)

Check:

Substitute \(y = 2.5\) back into the original equation:
Left side: \(4(2.5) - 1.3 = 10 - 1.3 = 8.7\)
Right side: \(8.7\)
Since left side = right side, \(y = 2.5\) is correct.

Answer:

\(x = 4\)

Problem 18: \(5y + 1.3 = 21.3\)