Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(3x+2)=9-(10+2x)\)
2. \(5(-3x-5)=14+(-3+x)\)
3. \(3(-2x-5)=-9-(-1-5x)\)
4. \(3(2x+2)=-3+(2+x)\)
5. \(2(-4x-5)=3+(14-5x)\)
6. \(5(6x+1)=-5+(7+x)\)
7. \(2(3x-7)=12-(13+x)\)
8. \(6(4x+4)=7+(11+x)\)
9. \(3(3x-2)=2-(-9+4x)\)
10. \(2(-x+5)=6+(-3+x)\)
11. \(5(5x+5)=-9-(-4-4x)\)
12. \(4(3x-1)=9+(-3+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+2)& = & 9 \color{red}{-} (10+2x) \\\Leftrightarrow & 9x+6& = &9-10-2x \\\Leftrightarrow & 9x \color{red}{+6} & = &-1 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & 9x+2x& = &-1-6 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-5)& = & 14 \color{red}{+} (-3+x) \\\Leftrightarrow & -15x-25& = &14-3+x \\\Leftrightarrow & -15x \color{red}{-25} & = &11 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -15x-x& = &11+25 \\\Leftrightarrow & -16x& = &36 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{36}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-5)& = & -9 \color{red}{-} (-1-5x) \\\Leftrightarrow & -6x-15& = &-9+1+5x \\\Leftrightarrow & -6x \color{red}{-15} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -6x-5x& = &-8+15 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+2)& = & -3 \color{red}{+} (2+x) \\\Leftrightarrow & 6x+6& = &-3+2+x \\\Leftrightarrow & 6x \color{red}{+6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &-1-6 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-5)& = & 3 \color{red}{+} (14-5x) \\\Leftrightarrow & -8x-10& = &3+14-5x \\\Leftrightarrow & -8x \color{red}{-10} & = &17 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & -8x+5x& = &17+10 \\\Leftrightarrow & -3x& = &27 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{27}{ \color{red}{-3} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+1)& = & -5 \color{red}{+} (7+x) \\\Leftrightarrow & 30x+5& = &-5+7+x \\\Leftrightarrow & 30x \color{red}{+5} & = &2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 30x-x& = &2-5 \\\Leftrightarrow & 29x& = &-3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x-7)& = & 12 \color{red}{-} (13+x) \\\Leftrightarrow & 6x-14& = &12-13-x \\\Leftrightarrow & 6x \color{red}{-14} & = &-1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 6x+x& = &-1+14 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+4)& = & 7 \color{red}{+} (11+x) \\\Leftrightarrow & 24x+24& = &7+11+x \\\Leftrightarrow & 24x \color{red}{+24} & = &18 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &18-24 \\\Leftrightarrow & 23x& = &-6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-2)& = & 2 \color{red}{-} (-9+4x) \\\Leftrightarrow & 9x-6& = &2+9-4x \\\Leftrightarrow & 9x \color{red}{-6} & = &11 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & 9x+4x& = &11+6 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x+5)& = & 6 \color{red}{+} (-3+x) \\\Leftrightarrow & -2x+10& = &6-3+x \\\Leftrightarrow & -2x \color{red}{+10} & = &3 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -2x-x& = &3-10 \\\Leftrightarrow & -3x& = &-7 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-7}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+5)& = & -9 \color{red}{-} (-4-4x) \\\Leftrightarrow & 25x+25& = &-9+4+4x \\\Leftrightarrow & 25x \color{red}{+25} & = &-5 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 25x-4x& = &-5-25 \\\Leftrightarrow & 21x& = &-30 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-30}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-1)& = & 9 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x-4& = &9-3+x \\\Leftrightarrow & 12x \color{red}{-4} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &6+4 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)