Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x+3)& = & -13 \color{red}{+} (1+x) \\\Leftrightarrow & -25x+15& = &-13+1+x \\\Leftrightarrow & -25x \color{red}{+15} & = &-12 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -25x-x& = &-12-15 \\\Leftrightarrow & -26x& = &-27 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-27}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{27}{26} & & \\ & V = \left\{ \frac{27}{26} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-2)& = & -9 \color{red}{-} (-6-3x) \\\Leftrightarrow & 10x-4& = &-9+6+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &-3+4 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+5)& = & 4 \color{red}{+} (-15+x) \\\Leftrightarrow & -10x+10& = &4-15+x \\\Leftrightarrow & -10x \color{red}{+10} & = &-11 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &-11-10 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-7)& = & -6 \color{red}{+} (-8-5x) \\\Leftrightarrow & 8x-14& = &-6-8-5x \\\Leftrightarrow & 8x \color{red}{-14} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & 8x+5x& = &-14+14 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+4)& = & 1 \color{red}{+} (-8+x) \\\Leftrightarrow & -8x+16& = &1-8+x \\\Leftrightarrow & -8x \color{red}{+16} & = &-7 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -8x-x& = &-7-16 \\\Leftrightarrow & -9x& = &-23 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-23}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x-3)& = & -3 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x-18& = &-3-6+x \\\Leftrightarrow & 24x \color{red}{-18} & = &-9 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &-9+18 \\\Leftrightarrow & 23x& = &9 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{9}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-7)& = & -7 \color{red}{+} (2-4x) \\\Leftrightarrow & 5x-35& = &-7+2-4x \\\Leftrightarrow & 5x \color{red}{-35} & = &-5 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &-5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & 5x+4x& = &-5+35 \\\Leftrightarrow & 9x& = &30 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{30}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-4)& = & 1 \color{red}{-} (2-2x) \\\Leftrightarrow & -15x-12& = &1-2+2x \\\Leftrightarrow & -15x \color{red}{-12} & = &-1 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & -15x-2x& = &-1+12 \\\Leftrightarrow & -17x& = &11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-5)& = & -6 \color{red}{-} (-12+x) \\\Leftrightarrow & 24x-30& = &-6+12-x \\\Leftrightarrow & 24x \color{red}{-30} & = &6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &6+30 \\\Leftrightarrow & 25x& = &36 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{36}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{36}{25} & & \\ & V = \left\{ \frac{36}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+6)& = & -2 \color{red}{-} (1+3x) \\\Leftrightarrow & 20x+24& = &-2-1-3x \\\Leftrightarrow & 20x \color{red}{+24} & = &-3 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 20x+3x& = &-3-24 \\\Leftrightarrow & 23x& = &-27 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-27}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-3)& = & -5 \color{red}{+} (15-5x) \\\Leftrightarrow & 6x-6& = &-5+15-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &10 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &10+6 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-3)& = & -11 \color{red}{-} (-3+x) \\\Leftrightarrow & -30x-18& = &-11+3-x \\\Leftrightarrow & -30x \color{red}{-18} & = &-8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &-8+18 \\\Leftrightarrow & -29x& = &10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-10}{29} & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)