Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-4)& = & 5 \color{red}{-} (-11+x) \\\Leftrightarrow & -10x-20& = &5+11-x \\\Leftrightarrow & -10x \color{red}{-20} & = &16 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -10x+x& = &16+20 \\\Leftrightarrow & -9x& = &36 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{36}{ \color{red}{-9} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x+7)& = & -6 \color{red}{-} (14+2x) \\\Leftrightarrow & 9x+21& = &-6-14-2x \\\Leftrightarrow & 9x \color{red}{+21} & = &-20 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &-20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 9x+2x& = &-20-21 \\\Leftrightarrow & 11x& = &-41 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-41}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-41}{11} & & \\ & V = \left\{ \frac{-41}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+2)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & -15x+6& = &-5-6+x \\\Leftrightarrow & -15x \color{red}{+6} & = &-11 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -15x-x& = &-11-6 \\\Leftrightarrow & -16x& = &-17 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-17}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{17}{16} & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x-1)& = & 7 \color{red}{-} (7-5x) \\\Leftrightarrow & -18x-3& = &7-7+5x \\\Leftrightarrow & -18x \color{red}{-3} & = &0 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -18x-5x& = &0+3 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-5)& = & 1 \color{red}{+} (4+x) \\\Leftrightarrow & 8x-10& = &1+4+x \\\Leftrightarrow & 8x \color{red}{-10} & = &5 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 8x-x& = &5+10 \\\Leftrightarrow & 7x& = &15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+6)& = & 3 \color{red}{-} (10+3x) \\\Leftrightarrow & -8x+12& = &3-10-3x \\\Leftrightarrow & -8x \color{red}{+12} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -8x+3x& = &-7-12 \\\Leftrightarrow & -5x& = &-19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-4)& = & -7 \color{red}{-} (4+3x) \\\Leftrightarrow & 8x-16& = &-7-4-3x \\\Leftrightarrow & 8x \color{red}{-16} & = &-11 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 8x+3x& = &-11+16 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-5)& = & 6 \color{red}{-} (15+x) \\\Leftrightarrow & 30x-30& = &6-15-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-9 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-9+30 \\\Leftrightarrow & 31x& = &21 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{21}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{21}{31} & & \\ & V = \left\{ \frac{21}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x+5)& = & -15 \color{red}{-} (11-5x) \\\Leftrightarrow & 8x+10& = &-15-11+5x \\\Leftrightarrow & 8x \color{red}{+10} & = &-26 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-26 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & 8x-5x& = &-26-10 \\\Leftrightarrow & 3x& = &-36 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-36}{ \color{red}{3} } \\\Leftrightarrow & x = -12 & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+7)& = & -5 \color{red}{-} (13-2x) \\\Leftrightarrow & -15x+21& = &-5-13+2x \\\Leftrightarrow & -15x \color{red}{+21} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & -15x-2x& = &-18-21 \\\Leftrightarrow & -17x& = &-39 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-39}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{39}{17} & & \\ & V = \left\{ \frac{39}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-6)& = & -5 \color{red}{+} (6-3x) \\\Leftrightarrow & -4x-12& = &-5+6-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &1 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &1+12 \\\Leftrightarrow & -x& = &13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{13}{ \color{red}{-1} } \\\Leftrightarrow & x = -13 & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-6)& = & -12 \color{red}{-} (10-4x) \\\Leftrightarrow & -5x-30& = &-12-10+4x \\\Leftrightarrow & -5x \color{red}{-30} & = &-22 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-22 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -5x-4x& = &-22+30 \\\Leftrightarrow & -9x& = &8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)