Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+6)& = & 2 \color{red}{+} (12-3x) \\\Leftrightarrow & 25x+30& = &2+12-3x \\\Leftrightarrow & 25x \color{red}{+30} & = &14 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 25x+3x& = &14-30 \\\Leftrightarrow & 28x& = &-16 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-16}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x+1)& = & -1 \color{red}{-} (15-3x) \\\Leftrightarrow & 4x+2& = &-1-15+3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 4x-3x& = &-16-2 \\\Leftrightarrow & x& = &-18 \\ & V = \left\{ -18 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+3)& = & 15 \color{red}{+} (-14+2x) \\\Leftrightarrow & -15x+9& = &15-14+2x \\\Leftrightarrow & -15x \color{red}{+9} & = &1 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -15x-2x& = &1-9 \\\Leftrightarrow & -17x& = &-8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{8}{17} & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x+7)& = & -14 \color{red}{-} (-9-3x) \\\Leftrightarrow & -10x+14& = &-14+9+3x \\\Leftrightarrow & -10x \color{red}{+14} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -10x-3x& = &-5-14 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-5)& = & -1 \color{red}{+} (-11-5x) \\\Leftrightarrow & -18x-15& = &-1-11-5x \\\Leftrightarrow & -18x \color{red}{-15} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -18x+5x& = &-12+15 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x-7)& = & 15 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x-21& = &15+9-x \\\Leftrightarrow & 12x \color{red}{-21} & = &24 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 12x+x& = &24+21 \\\Leftrightarrow & 13x& = &45 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{45}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{45}{13} & & \\ & V = \left\{ \frac{45}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+1)& = & 2 \color{red}{+} (-4-5x) \\\Leftrightarrow & -6x+3& = &2-4-5x \\\Leftrightarrow & -6x \color{red}{+3} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & -6x+5x& = &-2-3 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+5)& = & -3 \color{red}{+} (-12+x) \\\Leftrightarrow & 24x+30& = &-3-12+x \\\Leftrightarrow & 24x \color{red}{+30} & = &-15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 24x-x& = &-15-30 \\\Leftrightarrow & 23x& = &-45 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-45}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-45}{23} & & \\ & V = \left\{ \frac{-45}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-6)& = & 15 \color{red}{+} (9+x) \\\Leftrightarrow & -20x-24& = &15+9+x \\\Leftrightarrow & -20x \color{red}{-24} & = &24 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &24+24 \\\Leftrightarrow & -21x& = &48 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{48}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x-6)& = & 6 \color{red}{-} (15+x) \\\Leftrightarrow & -12x-24& = &6-15-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-9+24 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x+6)& = & 3 \color{red}{-} (11+x) \\\Leftrightarrow & 12x+18& = &3-11-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-8-18 \\\Leftrightarrow & 13x& = &-26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-26}{ \color{red}{13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x-3)& = & -14 \color{red}{+} (9+x) \\\Leftrightarrow & 15x-15& = &-14+9+x \\\Leftrightarrow & 15x \color{red}{-15} & = &-5 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 15x-x& = &-5+15 \\\Leftrightarrow & 14x& = &10 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{10}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)