Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-2)& = & 3 \color{red}{+} (8-5x) \\\Leftrightarrow & 3x-6& = &3+8-5x \\\Leftrightarrow & 3x \color{red}{-6} & = &11 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 3x+5x& = &11+6 \\\Leftrightarrow & 8x& = &17 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{17}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{17}{8} & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x+7)& = & 2 \color{red}{+} (-3+x) \\\Leftrightarrow & -30x+42& = &2-3+x \\\Leftrightarrow & -30x \color{red}{+42} & = &-1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -30x-x& = &-1-42 \\\Leftrightarrow & -31x& = &-43 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-43}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{43}{31} & & \\ & V = \left\{ \frac{43}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+4)& = & -10 \color{red}{+} (-15+2x) \\\Leftrightarrow & -25x+20& = &-10-15+2x \\\Leftrightarrow & -25x \color{red}{+20} & = &-25 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &-25 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -25x-2x& = &-25-20 \\\Leftrightarrow & -27x& = &-45 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-45}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x-2)& = & 13 \color{red}{-} (2+x) \\\Leftrightarrow & -5x-10& = &13-2-x \\\Leftrightarrow & -5x \color{red}{-10} & = &11 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -5x+x& = &11+10 \\\Leftrightarrow & -4x& = &21 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{21}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-21}{4} & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x+3)& = & 13 \color{red}{-} (3+x) \\\Leftrightarrow & 30x+18& = &13-3-x \\\Leftrightarrow & 30x \color{red}{+18} & = &10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &10-18 \\\Leftrightarrow & 31x& = &-8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+5)& = & 13 \color{red}{+} (11+x) \\\Leftrightarrow & -30x+30& = &13+11+x \\\Leftrightarrow & -30x \color{red}{+30} & = &24 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &24-30 \\\Leftrightarrow & -31x& = &-6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-5)& = & -6 \color{red}{+} (-12-5x) \\\Leftrightarrow & -18x-30& = &-6-12-5x \\\Leftrightarrow & -18x \color{red}{-30} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -18x+5x& = &-18+30 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-7)& = & 4 \color{red}{-} (3-2x) \\\Leftrightarrow & -3x-21& = &4-3+2x \\\Leftrightarrow & -3x \color{red}{-21} & = &1 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & -3x-2x& = &1+21 \\\Leftrightarrow & -5x& = &22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x+3)& = & 9 \color{red}{+} (-4+x) \\\Leftrightarrow & 8x+12& = &9-4+x \\\Leftrightarrow & 8x \color{red}{+12} & = &5 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &5-12 \\\Leftrightarrow & 7x& = &-7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-7}{ \color{red}{7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x+5)& = & -1 \color{red}{-} (9+x) \\\Leftrightarrow & 12x+15& = &-1-9-x \\\Leftrightarrow & 12x \color{red}{+15} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 12x+x& = &-10-15 \\\Leftrightarrow & 13x& = &-25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+5)& = & 13 \color{red}{-} (6+x) \\\Leftrightarrow & 36x+30& = &13-6-x \\\Leftrightarrow & 36x \color{red}{+30} & = &7 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 36x+x& = &7-30 \\\Leftrightarrow & 37x& = &-23 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-23}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-23}{37} & & \\ & V = \left\{ \frac{-23}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+6)& = & 12 \color{red}{+} (15+x) \\\Leftrightarrow & 20x+24& = &12+15+x \\\Leftrightarrow & 20x \color{red}{+24} & = &27 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 20x-x& = &27-24 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)