This week in math we covered solving one variable inequalities. This understanding is important because it ties in the aspects we learned earlier in the chapter and will continue to be put to use. I chose this topic because I understood how to solve this type of equation right away, as I was able to use the skills I have previously learned in this chapters.
Lets take a look at some examples…
Example a.
Step 1. My first step is to change the inequality into an equation with an ‘=’ sign so I can solve.
Step 2. I must now distribute the 2 to the terms inside the bracket.
Step 3. Now we rearrange so that the x values are to the left, and the constants to the left.
Step 4. Since I have a leading coefficent of 2 infront of my x value, I need to isolate the x by dividing both sides of the equation by 2. Finally it is important to substitute your inequality sign back in to get your final answer.
Example b.
Step 1. Our first step is to change the inequality to an equation.
Step 1. Since this example is written as a fraction, we want to eliminate the fraction by multiplying both sides of the equation by the denominator of 7. On the lefthand side, both 7s cancel out and on the right -3 is multilpied by 7 to get -21.
Step 3. Since the coefficent of x is one, we do not need to do any isolating; simply reearange the terms. X values to the left and constants to the right. Finally remember to change your ‘=’ sign back to an inequality.
Example C.
Step 1. As always, start by converting the inequality to an equation.
Step 2. Since in this example, both sides of the equation are written as fractions with different denominators we must multiply both sides of the equation by 21.
Step 3. Now that we have eliminated our fractions, we need to distribute the values outside our brackets to the inside terms.
Step 4. Finally we can rearrange. The x values to the left and constants to the right. Since the coefficent of x is 1, there is no need to isolate. Lastly, convert the equation back to an inequality.
Vocab :
Equation – contains an = sign.
Inequality – Compares two values, showing if one is less than, greater than, or simply not equal to another value.