Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+5)& = & 15 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+20& = &15+5+x \\\Leftrightarrow & 12x \color{red}{+20} & = &20 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 12x-x& = &20-20 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x-3)& = & 15 \color{red}{-} (-8+x) \\\Leftrightarrow & -6x-18& = &15+8-x \\\Leftrightarrow & -6x \color{red}{-18} & = &23 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -6x+x& = &23+18 \\\Leftrightarrow & -5x& = &41 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{41}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-41}{5} & & \\ & V = \left\{ \frac{-41}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+4)& = & -5 \color{red}{+} (-15+3x) \\\Leftrightarrow & -10x+8& = &-5-15+3x \\\Leftrightarrow & -10x \color{red}{+8} & = &-20 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -10x-3x& = &-20-8 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+1)& = & -5 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x+5& = &-5-1+x \\\Leftrightarrow & -30x \color{red}{+5} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -30x-x& = &-6-5 \\\Leftrightarrow & -31x& = &-11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+3)& = & 12 \color{red}{-} (-14+x) \\\Leftrightarrow & 4x+12& = &12+14-x \\\Leftrightarrow & 4x \color{red}{+12} & = &26 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 4x+x& = &26-12 \\\Leftrightarrow & 5x& = &14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+7)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & 20x+35& = &-13-4+x \\\Leftrightarrow & 20x \color{red}{+35} & = &-17 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &-17-35 \\\Leftrightarrow & 19x& = &-52 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-52}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-52}{19} & & \\ & V = \left\{ \frac{-52}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x+2)& = & 10 \color{red}{+} (1-3x) \\\Leftrightarrow & 10x+4& = &10+1-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &11 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &11-4 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-2)& = & -1 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x-12& = &-1-4+x \\\Leftrightarrow & -30x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &-5+12 \\\Leftrightarrow & -31x& = &7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-7}{31} & & \\ & V = \left\{ \frac{-7}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+6)& = & -13 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+18& = &-13-14-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-27 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-27-18 \\\Leftrightarrow & 13x& = &-45 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-45}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-45}{13} & & \\ & V = \left\{ \frac{-45}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-5)& = & 1 \color{red}{-} (2+x) \\\Leftrightarrow & 24x-30& = &1-2-x \\\Leftrightarrow & 24x \color{red}{-30} & = &-1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &-1+30 \\\Leftrightarrow & 25x& = &29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+2)& = & 5 \color{red}{-} (5+x) \\\Leftrightarrow & 4x+8& = &5-5-x \\\Leftrightarrow & 4x \color{red}{+8} & = &0 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 4x+x& = &0-8 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x-5)& = & -9 \color{red}{-} (-5+x) \\\Leftrightarrow & 15x-25& = &-9+5-x \\\Leftrightarrow & 15x \color{red}{-25} & = &-4 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 15x+x& = &-4+25 \\\Leftrightarrow & 16x& = &21 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{21}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{21}{16} & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)