Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x-7)& = & 11 \color{red}{+} (-12+x) \\\Leftrightarrow & 25x-35& = &11-12+x \\\Leftrightarrow & 25x \color{red}{-35} & = &-1 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 25x-x& = &-1+35 \\\Leftrightarrow & 24x& = &34 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{34}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{17}{12} & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x-4)& = & -1 \color{red}{+} (5-3x) \\\Leftrightarrow & 10x-20& = &-1+5-3x \\\Leftrightarrow & 10x \color{red}{-20} & = &4 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 10x+3x& = &4+20 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+4)& = & -10 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x+16& = &-10-3+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-13-16 \\\Leftrightarrow & -21x& = &-29 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-29}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+7)& = & 1 \color{red}{-} (15+x) \\\Leftrightarrow & -36x+42& = &1-15-x \\\Leftrightarrow & -36x \color{red}{+42} & = &-14 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -36x+x& = &-14-42 \\\Leftrightarrow & -35x& = &-56 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-56}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x+6)& = & 7 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+36& = &7+10+x \\\Leftrightarrow & 12x \color{red}{+36} & = &17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 12x-x& = &17-36 \\\Leftrightarrow & 11x& = &-19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+5)& = & 3 \color{red}{+} (-3+x) \\\Leftrightarrow & 3x+15& = &3-3+x \\\Leftrightarrow & 3x \color{red}{+15} & = &0 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 3x-x& = &0-15 \\\Leftrightarrow & 2x& = &-15 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-15}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-15}{2} & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x+6)& = & 8 \color{red}{+} (-13+4x) \\\Leftrightarrow & -15x+30& = &8-13+4x \\\Leftrightarrow & -15x \color{red}{+30} & = &-5 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & -15x-4x& = &-5-30 \\\Leftrightarrow & -19x& = &-35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-1)& = & 11 \color{red}{-} (-9+2x) \\\Leftrightarrow & 3x-3& = &11+9-2x \\\Leftrightarrow & 3x \color{red}{-3} & = &20 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 3x+2x& = &20+3 \\\Leftrightarrow & 5x& = &23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{23}{5} & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-3)& = & -9 \color{red}{-} (-12-5x) \\\Leftrightarrow & -16x-12& = &-9+12+5x \\\Leftrightarrow & -16x \color{red}{-12} & = &3 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -16x-5x& = &3+12 \\\Leftrightarrow & -21x& = &15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x+6)& = & 15 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x+36& = &15+11-x \\\Leftrightarrow & 30x \color{red}{+36} & = &26 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &26-36 \\\Leftrightarrow & 31x& = &-10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-1)& = & 2 \color{red}{+} (8+x) \\\Leftrightarrow & 15x-3& = &2+8+x \\\Leftrightarrow & 15x \color{red}{-3} & = &10 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 15x-x& = &10+3 \\\Leftrightarrow & 14x& = &13 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{13}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{13}{14} & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-x+7)& = & -13 \color{red}{+} (-6+x) \\\Leftrightarrow & -3x+21& = &-13-6+x \\\Leftrightarrow & -3x \color{red}{+21} & = &-19 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -3x-x& = &-19-21 \\\Leftrightarrow & -4x& = &-40 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-40}{ \color{red}{-4} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)