Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+6)& = & -5 \color{red}{+} (2+x) \\\Leftrightarrow & 20x+24& = &-5+2+x \\\Leftrightarrow & 20x \color{red}{+24} & = &-3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 20x-x& = &-3-24 \\\Leftrightarrow & 19x& = &-27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+1)& = & -14 \color{red}{-} (-14-2x) \\\Leftrightarrow & -15x+5& = &-14+14+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &0 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &0-5 \\\Leftrightarrow & -17x& = &-5 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-5}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-6)& = & -12 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x-30& = &-12-15+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-27 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-27+30 \\\Leftrightarrow & -31x& = &3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+7)& = & -1 \color{red}{+} (4+x) \\\Leftrightarrow & -30x+35& = &-1+4+x \\\Leftrightarrow & -30x \color{red}{+35} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &3-35 \\\Leftrightarrow & -31x& = &-32 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-32}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{32}{31} & & \\ & V = \left\{ \frac{32}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-5)& = & 1 \color{red}{-} (-14+x) \\\Leftrightarrow & -6x-30& = &1+14-x \\\Leftrightarrow & -6x \color{red}{-30} & = &15 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -6x+x& = &15+30 \\\Leftrightarrow & -5x& = &45 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{45}{ \color{red}{-5} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-1)& = & 12 \color{red}{-} (8+x) \\\Leftrightarrow & 30x-6& = &12-8-x \\\Leftrightarrow & 30x \color{red}{-6} & = &4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &4+6 \\\Leftrightarrow & 31x& = &10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+6)& = & 1 \color{red}{-} (7+x) \\\Leftrightarrow & 12x+36& = &1-7-x \\\Leftrightarrow & 12x \color{red}{+36} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &-6-36 \\\Leftrightarrow & 13x& = &-42 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-42}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-42}{13} & & \\ & V = \left\{ \frac{-42}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x+6)& = & 3 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x+18& = &3-6+x \\\Leftrightarrow & 12x \color{red}{+18} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &-3-18 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x+4)& = & 15 \color{red}{-} (-15+x) \\\Leftrightarrow & -18x+12& = &15+15-x \\\Leftrightarrow & -18x \color{red}{+12} & = &30 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &30 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -18x+x& = &30-12 \\\Leftrightarrow & -17x& = &18 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{18}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-18}{17} & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x-5)& = & 5 \color{red}{+} (-7-5x) \\\Leftrightarrow & 8x-10& = &5-7-5x \\\Leftrightarrow & 8x \color{red}{-10} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & 8x+5x& = &-2+10 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x-2)& = & -9 \color{red}{-} (5+x) \\\Leftrightarrow & 36x-12& = &-9-5-x \\\Leftrightarrow & 36x \color{red}{-12} & = &-14 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 36x+x& = &-14+12 \\\Leftrightarrow & 37x& = &-2 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-2}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-2}{37} & & \\ & V = \left\{ \frac{-2}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x-1)& = & -1 \color{red}{-} (10+x) \\\Leftrightarrow & 6x-3& = &-1-10-x \\\Leftrightarrow & 6x \color{red}{-3} & = &-11 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 6x+x& = &-11+3 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)