Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-5)& = & 13 \color{red}{-} (-8-3x) \\\Leftrightarrow & -10x-25& = &13+8+3x \\\Leftrightarrow & -10x \color{red}{-25} & = &21 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -10x-3x& = &21+25 \\\Leftrightarrow & -13x& = &46 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{46}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-46}{13} & & \\ & V = \left\{ \frac{-46}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-4)& = & 2 \color{red}{+} (-5+x) \\\Leftrightarrow & 5x-20& = &2-5+x \\\Leftrightarrow & 5x \color{red}{-20} & = &-3 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 5x-x& = &-3+20 \\\Leftrightarrow & 4x& = &17 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{17}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{17}{4} & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+2)& = & -1 \color{red}{+} (-13+3x) \\\Leftrightarrow & -10x+4& = &-1-13+3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-14 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -10x-3x& = &-14-4 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-2)& = & 3 \color{red}{-} (-1+x) \\\Leftrightarrow & 30x-12& = &3+1-x \\\Leftrightarrow & 30x \color{red}{-12} & = &4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &4+12 \\\Leftrightarrow & 31x& = &16 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{16}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{16}{31} & & \\ & V = \left\{ \frac{16}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-7)& = & -2 \color{red}{-} (12+x) \\\Leftrightarrow & -8x-14& = &-2-12-x \\\Leftrightarrow & -8x \color{red}{-14} & = &-14 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -8x+x& = &-14+14 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x-2)& = & -15 \color{red}{-} (1+x) \\\Leftrightarrow & -16x-8& = &-15-1-x \\\Leftrightarrow & -16x \color{red}{-8} & = &-16 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -16x+x& = &-16+8 \\\Leftrightarrow & -15x& = &-8 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-8}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+6)& = & -9 \color{red}{+} (8+x) \\\Leftrightarrow & -20x+24& = &-9+8+x \\\Leftrightarrow & -20x \color{red}{+24} & = &-1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &-1-24 \\\Leftrightarrow & -21x& = &-25 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-25}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{25}{21} & & \\ & V = \left\{ \frac{25}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+3)& = & -2 \color{red}{-} (10-5x) \\\Leftrightarrow & -6x+18& = &-2-10+5x \\\Leftrightarrow & -6x \color{red}{+18} & = &-12 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -6x-5x& = &-12-18 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+7)& = & -11 \color{red}{+} (6+4x) \\\Leftrightarrow & 15x+21& = &-11+6+4x \\\Leftrightarrow & 15x \color{red}{+21} & = &-5 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 15x-4x& = &-5-21 \\\Leftrightarrow & 11x& = &-26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-1)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & 18x-3& = &9-8-x \\\Leftrightarrow & 18x \color{red}{-3} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 18x+x& = &1+3 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-2)& = & -10 \color{red}{+} (-12-4x) \\\Leftrightarrow & -9x-6& = &-10-12-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-22 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &-22+6 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+2)& = & 10 \color{red}{+} (-5+3x) \\\Leftrightarrow & 10x+10& = &10-5+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &5 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &5-10 \\\Leftrightarrow & 7x& = &-5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)