Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x-5)& = & -10 \color{red}{-} (13+x) \\\Leftrightarrow & 6x-30& = &-10-13-x \\\Leftrightarrow & 6x \color{red}{-30} & = &-23 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 6x+x& = &-23+30 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-5)& = & 11 \color{red}{+} (10+4x) \\\Leftrightarrow & 25x-25& = &11+10+4x \\\Leftrightarrow & 25x \color{red}{-25} & = &21 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & 25x-4x& = &21+25 \\\Leftrightarrow & 21x& = &46 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{46}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+4)& = & -7 \color{red}{-} (-12+x) \\\Leftrightarrow & 16x+16& = &-7+12-x \\\Leftrightarrow & 16x \color{red}{+16} & = &5 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 16x+x& = &5-16 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x-4)& = & 5 \color{red}{-} (4+x) \\\Leftrightarrow & -30x-20& = &5-4-x \\\Leftrightarrow & -30x \color{red}{-20} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &1+20 \\\Leftrightarrow & -29x& = &21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-3)& = & -10 \color{red}{-} (11+x) \\\Leftrightarrow & 30x-18& = &-10-11-x \\\Leftrightarrow & 30x \color{red}{-18} & = &-21 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &-21+18 \\\Leftrightarrow & 31x& = &-3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+6)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & 3x+18& = &9-8-x \\\Leftrightarrow & 3x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 3x+x& = &1-18 \\\Leftrightarrow & 4x& = &-17 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-17}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-17}{4} & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+4)& = & 5 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x+20& = &5+14-x \\\Leftrightarrow & -30x \color{red}{+20} & = &19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -30x+x& = &19-20 \\\Leftrightarrow & -29x& = &-1 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-1}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+2)& = & 13 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x+4& = &13+14-x \\\Leftrightarrow & -12x \color{red}{+4} & = &27 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &27-4 \\\Leftrightarrow & -11x& = &23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x+7)& = & 12 \color{red}{-} (10+4x) \\\Leftrightarrow & -3x+21& = &12-10-4x \\\Leftrightarrow & -3x \color{red}{+21} & = &2 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -3x+4x& = &2-21 \\\Leftrightarrow & x& = &-19 \\ & V = \left\{ -19 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x+2)& = & 6 \color{red}{+} (10+3x) \\\Leftrightarrow & -5x+10& = &6+10+3x \\\Leftrightarrow & -5x \color{red}{+10} & = &16 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -5x-3x& = &16-10 \\\Leftrightarrow & -8x& = &6 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{6}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x+7)& = & -3 \color{red}{+} (13-2x) \\\Leftrightarrow & -5x+35& = &-3+13-2x \\\Leftrightarrow & -5x \color{red}{+35} & = &10 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -5x+2x& = &10-35 \\\Leftrightarrow & -3x& = &-25 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-25}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{25}{3} & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x+2)& = & 6 \color{red}{+} (13+x) \\\Leftrightarrow & -20x+10& = &6+13+x \\\Leftrightarrow & -20x \color{red}{+10} & = &19 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &19-10 \\\Leftrightarrow & -21x& = &9 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{9}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)