algebra 2 • modules 3 - 5 • are you ready? diagnostic\nfactor each expression.\n10. ( x ^ { 2 } - 2 x - 24…

algebra 2 • modules 3 - 5 • are you ready? diagnostic\nfactor each expression.\n10. ( x ^ { 2 } - 2 x - 24 )\n11. ( 2 x ^ { 2 } + 5 x - 12 )\nsolve each equation.\n12. ( - 2 ( x - 5 ) + 3 x = 7 - 4 ( x - 9 ) )\n13. ( x ^ { 2 } + x - 30 = 0 )\n14. ( 9 x ^ { 2 } = 36 )\n15. solve.\n( left{ \begin{array} { l } { y = 2 x - 2 } \\ { y = - x ^ { 2 } - 2 x + 3 } end{array} \right. )

algebra 2 • modules 3 - 5 • are you ready? diagnostic\nfactor each expression.\n10. ( x ^ { 2 } - 2 x - 24 )\n11. ( 2 x ^ { 2 } + 5 x - 12 )\nsolve each equation.\n12. ( - 2 ( x - 5 ) + 3 x = 7 - 4 ( x - 9 ) )\n13. ( x ^ { 2 } + x - 30 = 0 )\n14. ( 9 x ^ { 2 } = 36 )\n15. solve.\n( left{ \begin{array} { l } { y = 2 x - 2 } \\ { y = - x ^ { 2 } - 2 x + 3 } end{array} \right. )

Answer

Explanation:

Step1: Expand both sides of the equation

$$ \begin{align*} -2(x - 5)+3x&=7-4(x - 9)\ -2x+10 + 3x&=7-4x + 36\ x+10&=43-4x \end{align*} $$

Step2: Move the terms with (x) to one side

Add (4x) to both sides: $$ \begin{align*} x+4x+10&=43-4x+4x\ 5x+10&=43 \end{align*} $$

Step3: Isolate (x)

Subtract (10) from both sides: $$ \begin{align*} 5x+10-10&=43-10\ 5x&=33 \end{align*} $$ Divide both sides by (5): $$x=\frac{33}{5}=6.6$$

Answer:

(x = 6.6)