Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(-6x+7)=-4+(-14+x)\)
2. \(3(2x-2)=-11-(-1+x)\)
3. \(3(2x+4)=-14-(-3-5x)\)
4. \(6(2x-4)=-4+(-14+x)\)
5. \(3(-x+6)=7+(-10+2x)\)
6. \(5(-3x+6)=-4+(14+4x)\)
7. \(4(5x-6)=-3-(3+x)\)
8. \(2(x-3)=15-(10+3x)\)
9. \(3(-3x-5)=14+(12-2x)\)
10. \(6(5x-1)=12-(5+x)\)
11. \(4(-5x+6)=-9+(14+x)\)
12. \(6(3x-3)=10-(-13+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+7)& = & -4 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x+28& = &-4-14+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-18 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-18-28 \\\Leftrightarrow & -25x& = &-46 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-46}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{46}{25} & & \\ & V = \left\{ \frac{46}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-2)& = & -11 \color{red}{-} (-1+x) \\\Leftrightarrow & 6x-6& = &-11+1-x \\\Leftrightarrow & 6x \color{red}{-6} & = &-10 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 6x+x& = &-10+6 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x+4)& = & -14 \color{red}{-} (-3-5x) \\\Leftrightarrow & 6x+12& = &-14+3+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &-11-12 \\\Leftrightarrow & x& = &-23 \\ & V = \left\{ -23 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-4)& = & -4 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x-24& = &-4-14+x \\\Leftrightarrow & 12x \color{red}{-24} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &-18+24 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+6)& = & 7 \color{red}{+} (-10+2x) \\\Leftrightarrow & -3x+18& = &7-10+2x \\\Leftrightarrow & -3x \color{red}{+18} & = &-3 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & -3x-2x& = &-3-18 \\\Leftrightarrow & -5x& = &-21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+6)& = & -4 \color{red}{+} (14+4x) \\\Leftrightarrow & -15x+30& = &-4+14+4x \\\Leftrightarrow & -15x \color{red}{+30} & = &10 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & -15x-4x& = &10-30 \\\Leftrightarrow & -19x& = &-20 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-20}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{20}{19} & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-6)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & 20x-24& = &-3-3-x \\\Leftrightarrow & 20x \color{red}{-24} & = &-6 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &-6+24 \\\Leftrightarrow & 21x& = &18 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{18}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-3)& = & 15 \color{red}{-} (10+3x) \\\Leftrightarrow & 2x-6& = &15-10-3x \\\Leftrightarrow & 2x \color{red}{-6} & = &5 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & 2x+3x& = &5+6 \\\Leftrightarrow & 5x& = &11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-5)& = & 14 \color{red}{+} (12-2x) \\\Leftrightarrow & -9x-15& = &14+12-2x \\\Leftrightarrow & -9x \color{red}{-15} & = &26 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &26 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -9x+2x& = &26+15 \\\Leftrightarrow & -7x& = &41 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{41}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-41}{7} & & \\ & V = \left\{ \frac{-41}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x-1)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 30x-6& = &12-5-x \\\Leftrightarrow & 30x \color{red}{-6} & = &7 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &7+6 \\\Leftrightarrow & 31x& = &13 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{13}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{13}{31} & & \\ & V = \left\{ \frac{13}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+6)& = & -9 \color{red}{+} (14+x) \\\Leftrightarrow & -20x+24& = &-9+14+x \\\Leftrightarrow & -20x \color{red}{+24} & = &5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &5-24 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-3)& = & 10 \color{red}{-} (-13+x) \\\Leftrightarrow & 18x-18& = &10+13-x \\\Leftrightarrow & 18x \color{red}{-18} & = &23 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 18x+x& = &23+18 \\\Leftrightarrow & 19x& = &41 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{41}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{41}{19} & & \\ & V = \left\{ \frac{41}{19} \right\} & \\\end{align}\)