Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(5(-x+2)=15-(9+2x)\)
2. \(5(-6x-4)=-7+(1+x)\)
3. \(4(-2x-2)=13+(-11+x)\)
4. \(3(x-6)=11+(13+x)\)
5. \(2(3x-1)=1+(7+x)\)
6. \(6(-4x-7)=-11+(7+x)\)
7. \(5(-x-1)=8+(7-2x)\)
8. \(6(-x-1)=13-(2-5x)\)
9. \(2(2x+7)=-4+(-7+3x)\)
10. \(3(-3x+7)=-11-(11-2x)\)
11. \(3(3x-3)=-6-(7-4x)\)
12. \(6(3x-3)=-2+(-3+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x+2)& = & 15 \color{red}{-} (9+2x) \\\Leftrightarrow & -5x+10& = &15-9-2x \\\Leftrightarrow & -5x \color{red}{+10} & = &6 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & -5x+2x& = &6-10 \\\Leftrightarrow & -3x& = &-4 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-4}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x-4)& = & -7 \color{red}{+} (1+x) \\\Leftrightarrow & -30x-20& = &-7+1+x \\\Leftrightarrow & -30x \color{red}{-20} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &-6+20 \\\Leftrightarrow & -31x& = &14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x-2)& = & 13 \color{red}{+} (-11+x) \\\Leftrightarrow & -8x-8& = &13-11+x \\\Leftrightarrow & -8x \color{red}{-8} & = &2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -8x-x& = &2+8 \\\Leftrightarrow & -9x& = &10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-10}{9} & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x-6)& = & 11 \color{red}{+} (13+x) \\\Leftrightarrow & 3x-18& = &11+13+x \\\Leftrightarrow & 3x \color{red}{-18} & = &24 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 3x-x& = &24+18 \\\Leftrightarrow & 2x& = &42 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{42}{ \color{red}{2} } \\\Leftrightarrow & x = 21 & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x-1)& = & 1 \color{red}{+} (7+x) \\\Leftrightarrow & 6x-2& = &1+7+x \\\Leftrightarrow & 6x \color{red}{-2} & = &8 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 6x-x& = &8+2 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-7)& = & -11 \color{red}{+} (7+x) \\\Leftrightarrow & -24x-42& = &-11+7+x \\\Leftrightarrow & -24x \color{red}{-42} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &-4+42 \\\Leftrightarrow & -25x& = &38 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{38}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-38}{25} & & \\ & V = \left\{ \frac{-38}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-1)& = & 8 \color{red}{+} (7-2x) \\\Leftrightarrow & -5x-5& = &8+7-2x \\\Leftrightarrow & -5x \color{red}{-5} & = &15 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & -5x+2x& = &15+5 \\\Leftrightarrow & -3x& = &20 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{20}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-1)& = & 13 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x-6& = &13-2+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &11 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &11+6 \\\Leftrightarrow & -11x& = &17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x+7)& = & -4 \color{red}{+} (-7+3x) \\\Leftrightarrow & 4x+14& = &-4-7+3x \\\Leftrightarrow & 4x \color{red}{+14} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 4x-3x& = &-11-14 \\\Leftrightarrow & x& = &-25 \\ & V = \left\{ -25 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x+7)& = & -11 \color{red}{-} (11-2x) \\\Leftrightarrow & -9x+21& = &-11-11+2x \\\Leftrightarrow & -9x \color{red}{+21} & = &-22 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &-22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & -9x-2x& = &-22-21 \\\Leftrightarrow & -11x& = &-43 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-43}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{43}{11} & & \\ & V = \left\{ \frac{43}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-3)& = & -6 \color{red}{-} (7-4x) \\\Leftrightarrow & 9x-9& = &-6-7+4x \\\Leftrightarrow & 9x \color{red}{-9} & = &-13 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & 9x-4x& = &-13+9 \\\Leftrightarrow & 5x& = &-4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-3)& = & -2 \color{red}{+} (-3+x) \\\Leftrightarrow & 18x-18& = &-2-3+x \\\Leftrightarrow & 18x \color{red}{-18} & = &-5 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &-5+18 \\\Leftrightarrow & 17x& = &13 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{13}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{13}{17} & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)