Question 2.4.1: Solve: 2(x + 3) = 10....
Solve: 2(x + 3) = 10.
To solve the equation, we can use the distributive property to separate the terms on the left side of the equation.
Step 1:
Apply the distributive property: 2x + 6 = 10
Step 2:
Simplify the equation by adding -6 to both sides: 2x + 6 + (-6) = 10 + (-6) 2x = 4
Step 3:
Divide both sides of the equation by 2 to isolate the variable x: (1/2)(2x) = (1/2)(4) x = 2
Therefore, the solution to the equation is x = 2.
Final Answer
To begin, we apply the distributive property to the left side of the equation to separate terms:
\begin{aligned}2 x+6 & =10 & & \text { Distributive property } \\2 x+6+(-6) & =10+(-6) & & \text { Addition property of equality } \\2 x & =4 & & \\\frac{ 1 }{ 2 }(2 x) & =\frac{ 1 }{ 2 }(4) & & \text { Multiply each side by }\frac{1}{2} \\x & =2 & &\end{aligned}
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