Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+1)& = & -14 \color{red}{+} (-14-2x) \\\Leftrightarrow & 15x+3& = &-14-14-2x \\\Leftrightarrow & 15x \color{red}{+3} & = &-28 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &-28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 15x+2x& = &-28-3 \\\Leftrightarrow & 17x& = &-31 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-31}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-31}{17} & & \\ & V = \left\{ \frac{-31}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+1)& = & 14 \color{red}{-} (-7+3x) \\\Leftrightarrow & 5x+5& = &14+7-3x \\\Leftrightarrow & 5x \color{red}{+5} & = &21 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-5} \\\Leftrightarrow & 5x+3x& = &21-5 \\\Leftrightarrow & 8x& = &16 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{16}{ \color{red}{8} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x+2)& = & -9 \color{red}{+} (-13+4x) \\\Leftrightarrow & 15x+6& = &-9-13+4x \\\Leftrightarrow & 15x \color{red}{+6} & = &-22 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &-22 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & 15x-4x& = &-22-6 \\\Leftrightarrow & 11x& = &-28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-3)& = & -12 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-18& = &-12+13-5x \\\Leftrightarrow & 6x \color{red}{-18} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 6x+5x& = &1+18 \\\Leftrightarrow & 11x& = &19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-7)& = & 7 \color{red}{-} (7+x) \\\Leftrightarrow & -8x-28& = &7-7-x \\\Leftrightarrow & -8x \color{red}{-28} & = &0 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -8x+x& = &0+28 \\\Leftrightarrow & -7x& = &28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{28}{ \color{red}{-7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+2)& = & -3 \color{red}{+} (-13+x) \\\Leftrightarrow & -30x+12& = &-3-13+x \\\Leftrightarrow & -30x \color{red}{+12} & = &-16 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -30x-x& = &-16-12 \\\Leftrightarrow & -31x& = &-28 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-28}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-7)& = & -5 \color{red}{+} (-11+x) \\\Leftrightarrow & -24x-28& = &-5-11+x \\\Leftrightarrow & -24x \color{red}{-28} & = &-16 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -24x-x& = &-16+28 \\\Leftrightarrow & -25x& = &12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-12}{25} & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x+2)& = & -10 \color{red}{-} (8-5x) \\\Leftrightarrow & -3x+6& = &-10-8+5x \\\Leftrightarrow & -3x \color{red}{+6} & = &-18 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -3x-5x& = &-18-6 \\\Leftrightarrow & -8x& = &-24 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-24}{ \color{red}{-8} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x+4)& = & 1 \color{red}{-} (-3-5x) \\\Leftrightarrow & -18x+24& = &1+3+5x \\\Leftrightarrow & -18x \color{red}{+24} & = &4 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -18x-5x& = &4-24 \\\Leftrightarrow & -23x& = &-20 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-20}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{20}{23} & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-4)& = & 10 \color{red}{-} (8+3x) \\\Leftrightarrow & 4x-16& = &10-8-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &2+16 \\\Leftrightarrow & 7x& = &18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x-7)& = & -4 \color{red}{+} (13+x) \\\Leftrightarrow & -2x-14& = &-4+13+x \\\Leftrightarrow & -2x \color{red}{-14} & = &9 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -2x-x& = &9+14 \\\Leftrightarrow & -3x& = &23 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{23}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-23}{3} & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (2x+5)& = & -8 \color{red}{-} (-5-3x) \\\Leftrightarrow & 4x+10& = &-8+5+3x \\\Leftrightarrow & 4x \color{red}{+10} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 4x-3x& = &-3-10 \\\Leftrightarrow & x& = &-13 \\ & V = \left\{ -13 \right\} & \\\end{align}\)