Solving One-Step Equations with Different Number Types

8 Questions

For the equation x + 8 = 15, what is the value of x?

If x - 4 = 10, what is the value of x?

In one-step equations with decimals, what may make the steps more complex?

Having a higher number of digits after the decimal point

For the equation $3 imes 4 ext{ ÷ } 2 = x$, what is the value of x?

$6$

What different types of number values can be encountered when solving one-step equations?

Whole numbers, decimal numbers, fractional numbers

If $x + 3.25 = 8$, what is the value of x?

$4.75$

When solving one-step equations with fractions, which operation is more commonly used?

Multiplication

For the equation $7 - x = 2$, what is the value of x?

$5$

Study Notes

Solving One Step Equations Involves Different Types of Numbers

When solving one-step equations, you may encounter different types of number values—whole numbers, decimal numbers, and fractional numbers. Each type requires its own approach to solve them effectively. Let's explore these methods together.

Solving One-Step Equations with Whole Numbers

Whole number equations typically involve adding or subtracting two integers until they match the value given by the equation. For example, if your equation is (5 + x = 7), you would need to find the integer (\text{x}) such that when added to 5 equals 7. This means that (x = 2).

Solving One-Step Equations with Decimal Numbers

Decimals can also appear in simple linear equations like (5 - 1.75 = y). Here again, it involves finding a variable (\text{y}) which matches the difference between 5 and 1.75; therefore, (y = 3.25). These steps can become more complex depending on how many digits after the dot you have in your input values. However, the general principle remains similar: perform addition or subtraction operations on the decimal numbers to obtain the result on the other side of the equal sign.

Solving One-Step Equations with Fractional Numbers

Fractions require a slightly different method because they often involve multiplication or division operations instead of just plain arithmetic. An example might look something like this: (3 \times 8 \div 2 = x). To arrive at an answer here, we multiply both sides of the equation by 2 so as to cancel out the denominator from the divisor term on our left side of the equation. Then we get (3 \cdot 8 = x); thus (x = 24) is the solution. With fractions, remember always what operation needs to happen before anything else–multiplying, dividing, or neither? That will help you determine where to start first.

In summary, while each kind of number presents its unique challenges, the basic rule remains the same: simply manipulate symbols based on their mathematical properties to find variables in expressions such that they make sense within any particular context of the problem presented.