Question

Solve the following equation: $6z+10=-2$

Answer 1

Hint: To solve this question, we just need to rearrange the terms and simplify the given equation. To do so, we take the constant term 10 to the right-hand side of the equation. Then we divide both sides of the equation by 6 in order to obtain the solution for z.

Complete step by step solution:
The given question is a linear equation of first order. This means that the relationship between the variable and the constant is linear with no power terms involved. To solve this question, we first need to take all the constant terms to one side. We take the +10 term on the left-hand side to the right-hand side. We know that when we shift terms from one side of the equation to the other side, they change their sign. For example, if $a+b=0,$ then shifting b to the other side is given as $a=-b.$
Therefore shifting 10 to the other side,
$\Rightarrow 6z=-2-10$
We add both the terms on the right-hand side since they are of the same negative sign.
$\Rightarrow 6z=-12$
We now need to divide both sides of the equation by 6 to get the value of z.
$\Rightarrow \dfrac{6z}{6}=-\dfrac{12}{6}$
We know that 6 divided by 6 gives 1 and similarly -12 divided by 6 gives -2.
$\Rightarrow z=-2$
Hence, the value of z upon solving the equation $6z+10=-2$ is -2.

Note: We can solve this question by subtracting 10 from both sides initially instead of shifting or moving the 10 term to the right-hand side. Both these operations yield the same result and the given the same answer. Since this is a linear equation of first order, there can be only one value or solution for z.