Problem 41 Solve and check. $$2=x+7$$... [FREE SOLUTION]

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Chapter 5: Problem 41

Solve and check. $$2=x+7$$

Short Answer

Expert verified

The solution of $x$ is $-5$.

Step by step solution

Isolate x

We isolate $x$ by subtracting 7 from both sides of the equation. So, $2-7=x+7-7$. This simplifies to $-5=x$.

Check the solution

To check the solution, we substitute the value of $x$ into the original equation. $2=(-5)+7$. This simplifies to $2=2$, so the solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Algebraic Expressions

An algebraic expression is a mathematical phrase that contains numbers, variables, and operation symbols. Such expressions are essential in representing real-world problems and relationships in a symbolic form, setting the stage for solving equations. For instance, in the equation $2 = x + 7$, $x + 7$ is an algebraic expression that shows how two quantities, $x$ and 7, are summed to give 2.

When working with algebraic expressions, it's important to understand terms like coefficients, which are the numerical factors of variables (in this case, the coefficient of $x$ is implicitly 1), and constants, like the number 7 in the expression, which remain unchanged.

Isolate Variable

To solve an equation for a particular variable means to find the value of that variable which makes the equation true. Isolating a variable is the process of manipulating the equation to get the variable by itself on one side of the equality. This involves performing operations that 'undo' what has been done to the variable.

For example, in the equation $2 = x + 7$, we want to isolate $x$. To do this, we subtract 7 (the inverse operation of addition) from both sides to undo the addition of 7 to $x$. This results in $x$ being by itself on one side of the equation: $2 - 7 = x + 7 - 7$ simplifies to $x = -5$, which shows that $x$ is isolated.

Checking Solutions

Once a solution to an equation has been found, it's important to verify its correctness. Checking the solution means substituting the found value back into the original equation to see if it fulfills the equation. If after the substitution, both sides of the equation are equal, the solution is correct.

For our equation $2 = x + 7$, after isolating the variable, we find that $x = -5$. To check this, we replace $x$ in the original equation with $ -5$: $2 = (-5) + 7$. Simplifying the right side, $ -5 + 7$ equals 2, which matches the left side. This confirms that our solution $x = -5$ is indeed correct.

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91影视

Solve and check. $$2=x+7$$

Short Answer

Step by step solution

Isolate x

Check the solution

Key Concepts

Algebraic Expressions

Isolate Variable

Checking Solutions

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