Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+6)& = & -1 \color{red}{+} (5+x) \\\Leftrightarrow & -24x+24& = &-1+5+x \\\Leftrightarrow & -24x \color{red}{+24} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &4-24 \\\Leftrightarrow & -25x& = &-20 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-20}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+6)& = & -11 \color{red}{-} (-3+x) \\\Leftrightarrow & 20x+24& = &-11+3-x \\\Leftrightarrow & 20x \color{red}{+24} & = &-8 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 20x+x& = &-8-24 \\\Leftrightarrow & 21x& = &-32 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-32}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-32}{21} & & \\ & V = \left\{ \frac{-32}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-3)& = & 15 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-15& = &15-8+x \\\Leftrightarrow & -30x \color{red}{-15} & = &7 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &7+15 \\\Leftrightarrow & -31x& = &22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-22}{31} & & \\ & V = \left\{ \frac{-22}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+3)& = & -8 \color{red}{-} (-4+x) \\\Leftrightarrow & -6x+9& = &-8+4-x \\\Leftrightarrow & -6x \color{red}{+9} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -6x+x& = &-4-9 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-5)& = & -4 \color{red}{-} (-12-5x) \\\Leftrightarrow & 36x-30& = &-4+12+5x \\\Leftrightarrow & 36x \color{red}{-30} & = &8 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 36x-5x& = &8+30 \\\Leftrightarrow & 31x& = &38 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{38}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{38}{31} & & \\ & V = \left\{ \frac{38}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+2)& = & 14 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x+6& = &14-4+x \\\Leftrightarrow & 12x \color{red}{+6} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &10-6 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+6)& = & 7 \color{red}{-} (3-5x) \\\Leftrightarrow & 3x+18& = &7-3+5x \\\Leftrightarrow & 3x \color{red}{+18} & = &4 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 3x-5x& = &4-18 \\\Leftrightarrow & -2x& = &-14 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-14}{ \color{red}{-2} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+4)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & -6x+24& = &-5-6+x \\\Leftrightarrow & -6x \color{red}{+24} & = &-11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -6x-x& = &-11-24 \\\Leftrightarrow & -7x& = &-35 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-35}{ \color{red}{-7} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-4)& = & -11 \color{red}{+} (-4+x) \\\Leftrightarrow & 20x-20& = &-11-4+x \\\Leftrightarrow & 20x \color{red}{-20} & = &-15 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &-15+20 \\\Leftrightarrow & 19x& = &5 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{5}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+1)& = & 3 \color{red}{+} (8-5x) \\\Leftrightarrow & -8x+4& = &3+8-5x \\\Leftrightarrow & -8x \color{red}{+4} & = &11 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & -8x+5x& = &11-4 \\\Leftrightarrow & -3x& = &7 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{7}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x+7)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & 12x+21& = &10-3-x \\\Leftrightarrow & 12x \color{red}{+21} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &7-21 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-1)& = & -10 \color{red}{-} (-14+3x) \\\Leftrightarrow & 8x-4& = &-10+14-3x \\\Leftrightarrow & 8x \color{red}{-4} & = &4 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 8x+3x& = &4+4 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)