Question

Solve the following equation \[28 = 4 + 3(t + 5)\]

Answer 1

Hint: A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. To solve the equation, we need to follow a few steps.
First, we expand the terms within the brackets. Then we will take all the constants at one side and the variables on the other side. Finally, we can find the value of t.

Complete step-by-step answer:
The given equation is \[28 = 4 + 3(t + 5)\]
We have to find the solution. It means we have to find the value of t.
This a polynomial of one degree with one variable.
Here, \[28 = 4 + 3(t + 5)\]
We will expand the bracket. Then we get,
\[28 = 4 + 3t + 15\]
Then, we will take all the constants at one side and the variables on the other side.
\[3t = 28 - 15 - 4\]
Solving we get,
\[3t = 9\]
Then we will divide each side by 3.
\[t = \dfrac{9}{3} = 3\]

$\therefore $ The solution of the given equation is \[t = 3\].

Note: A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form \[ax + b = 0,a \ne 0\]
For a linear equation, we may add, subtract, multiply, or divide an equation by a number or an expression as long as we do the same thing to both sides of the equal sign.
The solution set consists of all values that make the equation true.
We can justify our answer by substituting \[t = 3\] in the above equation.
Here, RHS = \[4 + 3(t + 5) = 4 + 3(3 + 5) = 28\]
Here, LHS and RHS are equal. So, the solution is true.
This type of equation is known as a conditional equation. Since, the equation is true for only one solution.