Question

1. what is the value of y in the equation below?

2y + 3(y - 5) = 10

a. 5

b. -5

c. 3

d. -1

Explanation:

Step1: Expand the brackets

Using the distributive property \(a(b + c)=ab+ac\), we expand \(3(y - 5)\) to get \(3y-15\). So the equation becomes \(2y + 3y-15=10\).

Step2: Combine like terms

Combine the \(y\)-terms: \(2y+3y = 5y\). The equation is now \(5y-15 = 10\).

Step3: Isolate the variable term

Add 15 to both sides of the equation: \(5y-15 + 15=10 + 15\), which simplifies to \(5y=25\).

Step4: Solve for y

Divide both sides by 5: \(\frac{5y}{5}=\frac{25}{5}\), so \(y = 5\). Wait, but let's check again. Wait, no, wait: \(2y+3(y - 5)=10\)
Expand: \(2y + 3y-15=10\)
Combine like terms: \(5y-15 = 10\)
Add 15: \(5y=25\)
Divide by 5: \(y = 5\)? But let's substitute back. If \(y = 5\), then left side: \(2(5)+3(5 - 5)=10+0 = 10\), which matches the right side. Wait, but the options have a. 5. Wait, but maybe I made a mistake? Wait, no, the calculation seems correct. Wait, let's re - do the steps:

1. Start with \(2y+3(y - 5)=10\)
2. Distribute the 3: \(2y+3y-15 = 10\) (because \(3\times y=3y\) and \(3\times(- 5)=-15\))
3. Combine the \(y\) terms: \(2y + 3y=5y\), so \(5y-15 = 10\)
4. Add 15 to both sides: \(5y-15 + 15=10 + 15\) gives \(5y=25\)
5. Divide both sides by 5: \(y=\frac{25}{5}=5\)

When we substitute \(y = 5\) into the original equation:

Left - hand side: \(2(5)+3(5 - 5)=10+3\times0 = 10\), which is equal to the right - hand side (10). So the solution is \(y = 5\).

Answer:

a. 5