Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x+1)& = & -4 \color{red}{-} (1-5x) \\\Leftrightarrow & 3x+3& = &-4-1+5x \\\Leftrightarrow & 3x \color{red}{+3} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 3x-5x& = &-5-3 \\\Leftrightarrow & -2x& = &-8 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-8}{ \color{red}{-2} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x-4)& = & -11 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x-24& = &-11-8+x \\\Leftrightarrow & 12x \color{red}{-24} & = &-19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &-19+24 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-1)& = & 9 \color{red}{+} (5+4x) \\\Leftrightarrow & 25x-5& = &9+5+4x \\\Leftrightarrow & 25x \color{red}{-5} & = &14 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & 25x-4x& = &14+5 \\\Leftrightarrow & 21x& = &19 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{19}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-2x-4)& = & 11 \color{red}{+} (-2+x) \\\Leftrightarrow & -10x-20& = &11-2+x \\\Leftrightarrow & -10x \color{red}{-20} & = &9 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -10x-x& = &9+20 \\\Leftrightarrow & -11x& = &29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+4)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & -9x+12& = &6+10+x \\\Leftrightarrow & -9x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -9x-x& = &16-12 \\\Leftrightarrow & -10x& = &4 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{4}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+4)& = & -13 \color{red}{-} (-10+4x) \\\Leftrightarrow & 15x+20& = &-13+10-4x \\\Leftrightarrow & 15x \color{red}{+20} & = &-3 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 15x+4x& = &-3-20 \\\Leftrightarrow & 19x& = &-23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x-1)& = & 10 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-3& = &10-1+x \\\Leftrightarrow & 12x \color{red}{-3} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 12x-x& = &9+3 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x-7)& = & -3 \color{red}{+} (-9-3x) \\\Leftrightarrow & 25x-35& = &-3-9-3x \\\Leftrightarrow & 25x \color{red}{-35} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & 25x+3x& = &-12+35 \\\Leftrightarrow & 28x& = &23 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{23}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{23}{28} & & \\ & V = \left\{ \frac{23}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x-5)& = & -14 \color{red}{+} (7+x) \\\Leftrightarrow & -30x-30& = &-14+7+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-7 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-7+30 \\\Leftrightarrow & -31x& = &23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-23}{31} & & \\ & V = \left\{ \frac{-23}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+4)& = & 8 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x+20& = &8+9-x \\\Leftrightarrow & 30x \color{red}{+20} & = &17 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &17-20 \\\Leftrightarrow & 31x& = &-3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x-1)& = & 9 \color{red}{-} (10+x) \\\Leftrightarrow & 12x-6& = &9-10-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-1+6 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+5)& = & -12 \color{red}{-} (1-2x) \\\Leftrightarrow & -15x+25& = &-12-1+2x \\\Leftrightarrow & -15x \color{red}{+25} & = &-13 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{-2x} & = &-13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-25} \\\Leftrightarrow & -15x-2x& = &-13-25 \\\Leftrightarrow & -17x& = &-38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{38}{17} & & \\ & V = \left\{ \frac{38}{17} \right\} & \\\end{align}\)