Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(3x+5)=15-(-3-5x)\)
2. \(3(-3x-2)=-1+(10+2x)\)
3. \(4(-3x-3)=5-(3+x)\)
4. \(2(6x-1)=5+(-11+x)\)
5. \(3(-x+7)=4+(-9-5x)\)
6. \(3(6x-3)=11+(7-5x)\)
7. \(3(x+7)=-4+(6+4x)\)
8. \(2(6x-5)=-9-(3+x)\)
9. \(6(4x+2)=-14+(-14+x)\)
10. \(5(6x-5)=7+(-10+x)\)
11. \(4(6x-5)=12+(-14+x)\)
12. \(3(-x-5)=-14-(6+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+5)& = & 15 \color{red}{-} (-3-5x) \\\Leftrightarrow & 18x+30& = &15+3+5x \\\Leftrightarrow & 18x \color{red}{+30} & = &18 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & 18x-5x& = &18-30 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x-2)& = & -1 \color{red}{+} (10+2x) \\\Leftrightarrow & -9x-6& = &-1+10+2x \\\Leftrightarrow & -9x \color{red}{-6} & = &9 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -9x-2x& = &9+6 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-3)& = & 5 \color{red}{-} (3+x) \\\Leftrightarrow & -12x-12& = &5-3-x \\\Leftrightarrow & -12x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &2+12 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x-1)& = & 5 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x-2& = &5-11+x \\\Leftrightarrow & 12x \color{red}{-2} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &-6+2 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+7)& = & 4 \color{red}{+} (-9-5x) \\\Leftrightarrow & -3x+21& = &4-9-5x \\\Leftrightarrow & -3x \color{red}{+21} & = &-5 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -3x+5x& = &-5-21 \\\Leftrightarrow & 2x& = &-26 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-26}{ \color{red}{2} } \\\Leftrightarrow & x = -13 & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-3)& = & 11 \color{red}{+} (7-5x) \\\Leftrightarrow & 18x-9& = &11+7-5x \\\Leftrightarrow & 18x \color{red}{-9} & = &18 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 18x+5x& = &18+9 \\\Leftrightarrow & 23x& = &27 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{27}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{27}{23} & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+7)& = & -4 \color{red}{+} (6+4x) \\\Leftrightarrow & 3x+21& = &-4+6+4x \\\Leftrightarrow & 3x \color{red}{+21} & = &2 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 3x-4x& = &2-21 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-5)& = & -9 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-10& = &-9-3-x \\\Leftrightarrow & 12x \color{red}{-10} & = &-12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 12x+x& = &-12+10 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+2)& = & -14 \color{red}{+} (-14+x) \\\Leftrightarrow & 24x+12& = &-14-14+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-28 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-28-12 \\\Leftrightarrow & 23x& = &-40 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-40}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-5)& = & 7 \color{red}{+} (-10+x) \\\Leftrightarrow & 30x-25& = &7-10+x \\\Leftrightarrow & 30x \color{red}{-25} & = &-3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 30x-x& = &-3+25 \\\Leftrightarrow & 29x& = &22 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{22}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{22}{29} & & \\ & V = \left\{ \frac{22}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x-5)& = & 12 \color{red}{+} (-14+x) \\\Leftrightarrow & 24x-20& = &12-14+x \\\Leftrightarrow & 24x \color{red}{-20} & = &-2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &-2+20 \\\Leftrightarrow & 23x& = &18 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{18}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{18}{23} & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-x-5)& = & -14 \color{red}{-} (6+x) \\\Leftrightarrow & -3x-15& = &-14-6-x \\\Leftrightarrow & -3x \color{red}{-15} & = &-20 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -3x+x& = &-20+15 \\\Leftrightarrow & -2x& = &-5 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-5}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)