Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x-2)& = & -3 \color{red}{+} (9-5x) \\\Leftrightarrow & -8x-8& = &-3+9-5x \\\Leftrightarrow & -8x \color{red}{-8} & = &6 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -8x+5x& = &6+8 \\\Leftrightarrow & -3x& = &14 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{14}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-6)& = & -1 \color{red}{+} (-14-2x) \\\Leftrightarrow & -5x-30& = &-1-14-2x \\\Leftrightarrow & -5x \color{red}{-30} & = &-15 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -5x+2x& = &-15+30 \\\Leftrightarrow & -3x& = &15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{15}{ \color{red}{-3} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x+5)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+20& = &-2+4+x \\\Leftrightarrow & 12x \color{red}{+20} & = &2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 12x-x& = &2-20 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+2)& = & 15 \color{red}{+} (11+x) \\\Leftrightarrow & -12x+6& = &15+11+x \\\Leftrightarrow & -12x \color{red}{+6} & = &26 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &26-6 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+4)& = & 12 \color{red}{-} (15+4x) \\\Leftrightarrow & -9x+12& = &12-15-4x \\\Leftrightarrow & -9x \color{red}{+12} & = &-3 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & -9x+4x& = &-3-12 \\\Leftrightarrow & -5x& = &-15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-15}{ \color{red}{-5} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x+1)& = & -11 \color{red}{-} (-3+x) \\\Leftrightarrow & 6x+3& = &-11+3-x \\\Leftrightarrow & 6x \color{red}{+3} & = &-8 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 6x+x& = &-8-3 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x+1)& = & 5 \color{red}{-} (4+x) \\\Leftrightarrow & -10x+2& = &5-4-x \\\Leftrightarrow & -10x \color{red}{+2} & = &1 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -10x+x& = &1-2 \\\Leftrightarrow & -9x& = &-1 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-1}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+4)& = & 9 \color{red}{+} (8+x) \\\Leftrightarrow & 16x+16& = &9+8+x \\\Leftrightarrow & 16x \color{red}{+16} & = &17 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 16x-x& = &17-16 \\\Leftrightarrow & 15x& = &1 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{1}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-2)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & -2x-4& = &-7-12+x \\\Leftrightarrow & -2x \color{red}{-4} & = &-19 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &-19+4 \\\Leftrightarrow & -3x& = &-15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-15}{ \color{red}{-3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x+2)& = & 3 \color{red}{+} (3-3x) \\\Leftrightarrow & -4x+4& = &3+3-3x \\\Leftrightarrow & -4x \color{red}{+4} & = &6 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -4x+3x& = &6-4 \\\Leftrightarrow & -x& = &2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{2}{ \color{red}{-1} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+4)& = & 2 \color{red}{+} (9-3x) \\\Leftrightarrow & 10x+8& = &2+9-3x \\\Leftrightarrow & 10x \color{red}{+8} & = &11 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 10x+3x& = &11-8 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+6)& = & -9 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x+24& = &-9-4+x \\\Leftrightarrow & -20x \color{red}{+24} & = &-13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &-13-24 \\\Leftrightarrow & -21x& = &-37 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-37}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{37}{21} & & \\ & V = \left\{ \frac{37}{21} \right\} & \\\end{align}\)