Answer:
x = 200
Step-by-step explanation:
Given equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]
Steps:
1. Substitute 15 as the value of y in the equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]
2. Add 10 to both sides:
[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]
3. Multiply both sides by 5 to isolate x:
[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]
4. Check your work:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]
Learn more here:
https://brainly.com/question/12965239
Hey there!
[tex] \boxed{\bold{\green{ x = 200}}} [/tex]
[tex] \\ [/tex]
Given expression :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]
1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
[tex] \\ [/tex]
2) Solve for x :
[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
⇢Add 10 to both sides of the equation :
[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
⇢Multiply both sides of the equation by 5:
[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]
[tex] \\ [/tex]
3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :
[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]
[tex] \\ \\ [/tex]
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