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Chapter 5: Problem 303

In the following exercises, solve the equation. $$ m-0.25=-1.67 $$

Short Answer

Expert verified
m = -1.42

Step by step solution

01

Add 0.25 to Both Sides

To isolate the variable m, add 0.25 to both sides of the equation. \[ m - 0.25 + 0.25 = -1.67 + 0.25 \]
02

Simplify the Right Side

Combine the numbers on the right side of the equation. \[ -1.67 + 0.25 = -1.42 \]
03

Write the Final Equation

After simplifying, you get: \[ m = -1.42 \]

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Key Concepts

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

Isolating Variables
In algebra, the goal is often to solve for an unknown variable. This is known as 'isolating the variable.' To isolate a variable, you need to get the variable by itself on one side of the equation. For example, in the equation:
\[ m - 0.25 = -1.67 \]we want to isolate 'm'. To do this, we need to move all other numbers to the other side of the equation. This often involves doing the opposite operation.
  • If you see subtraction, you'll add.
  • If you see multiplication, you'll divide.
For our exercise, we see subtraction (\( -0.25 \)). So, we add 0.25 to both sides. This helps to keep the equation balanced.

Isolating variables is crucial because it allows us to find the value of the unknown variable. Once 'm' is by itself, you have solved the equation.
Simplifying Equations
Simplifying equations makes them easier to understand and solve. This process involves combining like terms or simplifying operations. Continuing our example:
\[ m - 0.25 = -1.67 \]We've added 0.25 to both sides, so our equation now looks like:
\[ m = -1.67 + 0.25 \]
  • Next, you need to carry out the addition on the right side to simplify it further.
Think of simplifying as tidying up. It turns complicated equations into straightforward statements. This makes it easy to see what values you're working with.
  • After performing the addition, we get:
\[ m = -1.42 \]So, simplifying involves condensing the equation to a clearer form. This step is necessary to find your final answer.
Adding Decimals
Adding decimals is an important skill in solving equations like ours. When combining decimals, it's crucial to align them by their decimal points for accuracy. Let's look at our equation again:
\[ -1.67 + 0.25 \]Line them up so that the decimal points match vertically:
  • -1.67
  • + 0.25
Next, add digits column by column, starting from the rightmost digit.
  • 7 + 5 = 12 (write down the 2 and carry over 1)
  • 6 + 2 = 8, plus 1 (carryover) = 9
  • 1 + 0 = 1
Write down the decimal point in the same column as the original numbers. The result is:
\[ -1.67 + 0.25 = -1.42 \]When you add decimals carefully, you ensure the numbers are accurate. This precision is necessary to solve equations correctly. It鈥檚 a great way to make sure your math foundation is strong!

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