INPUT ARTICLE: Article: 5(x+4)=6x5{\displaystyle 5(x+4)=6x-5}. Use the distributive property to cancel the parentheses:5(x+4)=6x5{\displaystyle 5(x+4)=6x-5}5x+20=6x5{\displaystyle 5x+20=6x-5} Cancel the 5x{\displaystyle 5x} on the left side of the equation by subtracting 5x{\displaystyle 5x} from both sides:5x+20=6x5{\displaystyle 5x+20=6x-5}5x+205x=6x55x{\displaystyle 5x+20-5x=6x-5-5x}20=x5{\displaystyle 20=x-5} Isolate the variable by adding 5 to each side of the equation:20=x5{\displaystyle 20=x-5}20+5=x5+5{\displaystyle 20+5=x-5+5}25=x{\displaystyle 25=x} 7+3x=7x2{\displaystyle -7+3x={
rac {7-x}{2}}}. Remove the fraction. To do this, multiply each side of the equation by the fraction's denominator:7+3x=7x2{\displaystyle -7+3x={
rac {7-x}{2}}}2(7+3x)=2(7x2){\displaystyle 2(-7+3x)=2({
rac {7-x}{2}})}14+6x=7x{\displaystyle -14+6x=7-x} Cancel the x{\displaystyle -x} on the right side of the equation by adding x{\displaystyle x} to each side of the equation:14+6x=7x{\displaystyle -14+6x=7-x}14+6x+x=7x+x{\displaystyle -14+6x+x=7-x+x}14+7x=7{\displaystyle -14+7x=7} Move the constants to one side of the equation by adding 14 to each side:14+7x=7{\displaystyle -14+7x=7}14+7x+14=7+14{\displaystyle -14+7x+14=7+14}7x=21{\displaystyle 7x=21} Cancel the coefficient by dividing each side of the equation by 7:7x=21{\displaystyle 7x=21}7x7=217{\displaystyle {
rac {7x}{7}}={
rac {21}{7}}}x=3{\displaystyle x=3} 9x+15=12y;9y=9x+27{\displaystyle 9x+15=12y;9y=9x+27} Isolate the y{\displaystyle y} variable in the second equation:9y=9x+27{\displaystyle 9y=9x+27}9y=9(x+3){\displaystyle 9y=9(x+3)}9y9=9(x+3)9{\displaystyle {
rac {9y}{9}}={
rac {9(x+3)}{9}}}y=x+3{\displaystyle y=x+3} Plug in x+3{\displaystyle x+3} for y{\displaystyle y} in the first equation:9x+15=12y{\displaystyle 9x+15=12y}9x+15=12(x+3){\displaystyle 9x+15=12(x+3)} Use the distributive property to cancel the parentheses:9x+15=12x+36{\displaystyle 9x+15=12x+36} Cancel the variable on the left side of the equation by subtracting 9x{\displaystyle 9x} from each side:9x+15=12x+36{\displaystyle 9x+15=12x+36}9x+159x=12x+369x{\displaystyle 9x+15-9x=12x+36-9x}15=3x+36{\displaystyle 15=3x+36} Move the constants to one side by subtracting 36 from each side:15=3x+36{\displaystyle 15=3x+36}1536=3x+3636{\displaystyle 15-36=3x+36-36}21=3x{\displaystyle -21=3x} Cancel the coefficient by dividing each side by 3:21=3x{\displaystyle -21=3x}213=3x3{\displaystyle {
rac {-21}{3}}={
rac {3x}{3}}}7=x{\displaystyle -7=x} Solve for y{\displaystyle y} by plugging the value of x{\displaystyle x} into either equation:9y=9x+27{\displaystyle 9y=9x+27}9y=9(7)+27{\displaystyle 9y=9(-7)+27}9y=63+27{\displaystyle 9y=-63+27}9y=36{\displaystyle 9y=-36}9y9=369{\displaystyle {
rac {9y}{9}}={
rac {-36}{9}}}y=4{\displaystyle y=-4}

SUMMARY: Try this problem using the distributive property with one variable: Try this problem involving a fraction: Try solving this system of equations:

INPUT ARTICLE: Article: If you have been served with a summons and petition, you are the respondent in a court case for legal separation. The Respondent has several options: Do nothing. If the Respondent does not file a response within 30 days of being served, then the court will probably grant everything the Petitioner requested in the Petition for Legal Separation, including property division, support, and child custody and visitation. Make a written and notarized agreement. Instead of the Respondent filing a response to the Petition for Legal Separation, the parties can write an agreement, sign it, and have it notarized. The agreement should state that the parties agree to end the marriage or domestic partnership, and specify how the parties would like to divide their property, whether anyone will pay spousal support, and what child support, custody, and visitation orders are needed.The California courts provide more information on these agreements here. File a response, but also make a written and notarized agreement. If the Respondent files a response to the Petition for Legal Separation, the parties can still agree to resolve the issues and submit a written and notarized agreement. File a response without an agreement. By filing a response, the Respondent demonstrates that he or she disagrees with the requests that the Petitioner made in the Petition for Legal Separation. Any response must be filed within 30 days of the date that the Respondent was served with the Summons and Petition. This form, numbered FL-120, briefly identifies the issues the Respondent wants the court to address, including child custody, child and spousal support, and property division. You can download an FL-120 here. If you need help completing this form, read these instructions provided by the California courts. This form, numbered FL-105, informs the court of where any children are living and whether they are involved in other court cases. You can download an FL-105 here. The process and standards for applying for a fee waiver as a respondent are the same as those used for the petitioner. Some counties require respondents to file additional local forms for a legal separation, which may differ from those required of the petitioner. Check with your Family Law Facilitator or your county court's website. You can locate your county court's website by selecting your county on the California court's Find My Court webpage. If you are applying for a Fee Waiver, do not serve it on the other party.

SUMMARY:
Understand the Respondent's options. Fill out a Response. Fill out a Declaration Under Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA) only if you have any minor children with the Petitioner. Fill out a Fee Waiver if you cannot afford to pay the filing fee. Fill out any required local forms. File your forms with the court and have them served on the other party.