Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+1)& = & 12 \color{red}{+} (2-5x) \\\Leftrightarrow & -6x+2& = &12+2-5x \\\Leftrightarrow & -6x \color{red}{+2} & = &14 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-2} \\\Leftrightarrow & -6x+5x& = &14-2 \\\Leftrightarrow & -x& = &12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{12}{ \color{red}{-1} } \\\Leftrightarrow & x = -12 & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (3x+1)& = & -8 \color{red}{+} (8+4x) \\\Leftrightarrow & 15x+5& = &-8+8+4x \\\Leftrightarrow & 15x \color{red}{+5} & = &0 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 15x-4x& = &0-5 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-6)& = & 13 \color{red}{+} (2+x) \\\Leftrightarrow & -20x-30& = &13+2+x \\\Leftrightarrow & -20x \color{red}{-30} & = &15 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -20x-x& = &15+30 \\\Leftrightarrow & -21x& = &45 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{45}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-7)& = & -15 \color{red}{-} (14+x) \\\Leftrightarrow & -18x-42& = &-15-14-x \\\Leftrightarrow & -18x \color{red}{-42} & = &-29 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-29 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -18x+x& = &-29+42 \\\Leftrightarrow & -17x& = &13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-1)& = & 4 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x-6& = &4-14+x \\\Leftrightarrow & 30x \color{red}{-6} & = &-10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &-10+6 \\\Leftrightarrow & 29x& = &-4 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-4}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-4}{29} & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-5)& = & 2 \color{red}{+} (3-4x) \\\Leftrightarrow & -25x-25& = &2+3-4x \\\Leftrightarrow & -25x \color{red}{-25} & = &5 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -25x+4x& = &5+25 \\\Leftrightarrow & -21x& = &30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-x-4)& = & 12 \color{red}{-} (-14-5x) \\\Leftrightarrow & -6x-24& = &12+14+5x \\\Leftrightarrow & -6x \color{red}{-24} & = &26 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &26 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -6x-5x& = &26+24 \\\Leftrightarrow & -11x& = &50 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{50}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-50}{11} & & \\ & V = \left\{ \frac{-50}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+2)& = & 10 \color{red}{-} (-15-5x) \\\Leftrightarrow & 18x+6& = &10+15+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &25 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &25 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &25-6 \\\Leftrightarrow & 13x& = &19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-6)& = & -5 \color{red}{+} (7+x) \\\Leftrightarrow & -12x-12& = &-5+7+x \\\Leftrightarrow & -12x \color{red}{-12} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &2+12 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-2)& = & -11 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x-10& = &-11+12-x \\\Leftrightarrow & 30x \color{red}{-10} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &1+10 \\\Leftrightarrow & 31x& = &11 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{11}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-2x-1)& = & 3 \color{red}{+} (2-3x) \\\Leftrightarrow & -10x-5& = &3+2-3x \\\Leftrightarrow & -10x \color{red}{-5} & = &5 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -10x+3x& = &5+5 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x+7)& = & -9 \color{red}{-} (-9-3x) \\\Leftrightarrow & -4x+14& = &-9+9+3x \\\Leftrightarrow & -4x \color{red}{+14} & = &0 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -4x-3x& = &0-14 \\\Leftrightarrow & -7x& = &-14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-14}{ \color{red}{-7} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)