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Equations

1. 1.
2. 2.
3. 3. <ul><li>3X – 7 = X + 5 </li></ul><ul><li>LEFT SIDE RIGHT SIDE </li></ul>
4. 4. <ul><li>3X – 7 = X + 5 </li></ul><ul><li>TERMS : 3X; 7; X; 5 </li></ul><ul><li>VARIABLE : X </li></ul><ul><li>COEFFICIENTS : 3 AND 1 </li></ul><ul><li>CONSTANTS : 7 AND 5 </li></ul>
5. 5. <ul><li>The degree of an equation that has not more than one variable in each term is the exponent of the highest power to which that variable is raised in the equation. </li></ul><ul><li>The equation     3x - 17=0 is a FIRST-DEGREE equation, since x is raised only to the first power. </li></ul>
6. 6. <ul><li>Solving an equation for one variable means finding the value of the variable that makes the equation true. </li></ul><ul><li>For example, 11 is the SOLUTION of </li></ul><ul><li>x - 7 = 4 </li></ul><ul><li>since 11 - 7 = 4. </li></ul><ul><li>The number 11 is said to SATISFY the equation </li></ul>
7. 7. <ul><li>Two equations are equivalent if they have the same </li></ul><ul><li>solution </li></ul><ul><li>We can create equivalent equations using the following methods: </li></ul><ul><ul><li>Add or subtract the same quantity on either side of an </li></ul></ul><ul><ul><li>equation </li></ul></ul><ul><ul><li>Multiply or divide both sides of an equation by the same </li></ul></ul><ul><ul><li>quantity.         </li></ul></ul>
8. 8. <ul><li>Let’s create equations equivalent to 5x = 20 using the methods </li></ul><ul><li>mentioned above ·  Add 3 to each side </li></ul><ul><li>5x + 3 = 20 + 3 gives rise to 5x + 3 = 23 ·  Subtract 2 from each side </li></ul><ul><li>5x – 2 = 20 – 2 produces an equivalent equation 5x – 2 = 18 ·  Multiply each side by 4. </li></ul><ul><li>5x · 4 = 20 · 4 gives rise to 20x = 80 ·  Divide each side by 5.   </li></ul><ul><li>5x ÷ 5 = 20 ÷ 5 gives rise to an equivalent equation x = 4 </li></ul>
9. 9. <ul><li>In general, to solve an equation the following steps must be followed: </li></ul><ul><li>1. Remove parentheses. </li></ul><ul><li>2. Remove denominators. </li></ul><ul><li>3. Group the terms of x in one side and the independent terms in the other. </li></ul><ul><li>4. Reduce similar terms. </li></ul><ul><li>5. Solve for the unknown. </li></ul>
10. 10. <ul><li>2X – 3 = 6 + X </li></ul><ul><li>Group the similar terms, and then add: </li></ul><ul><li>2X – X = 6 + 3 </li></ul><ul><li>x = 9 </li></ul>
11. 11. <ul><li>2(2X – 3) = 6+ X </li></ul><ul><li>Remove parentheses: </li></ul><ul><li>4X – 6 = 6 + X </li></ul><ul><li>Group the terms and add: </li></ul><ul><li>4X – X = 6 + 6 </li></ul><ul><li>3X = 12 </li></ul><ul><li>If both sides of the equation are divided by 3, the solution is obtained: </li></ul><ul><li>X = 4 </li></ul>
12. 12. <ul><li>Jeanne has \$17 in her piggy bank. How much money does she need to buy a game that costs \$68? </li></ul><ul><li>Solution:    </li></ul><ul><li>Let x represent the amount of money Jeanne needs. </li></ul><ul><li>The following equation can represent this problem: </li></ul><ul><li>  </li></ul><ul><li>17 + x = 68 </li></ul><ul><li>  </li></ul><ul><li>We can subtract 17 from both sides of the equation to </li></ul><ul><li>find the value of x. </li></ul><ul><li>68 - 17 = x </li></ul><ul><li>Answer :    </li></ul><ul><li>x = 51, so Jeanne needs \$51 to buy the game. </li></ul>