Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x-5)& = & 10 \color{red}{-} (-6+x) \\\Leftrightarrow & -15x-15& = &10+6-x \\\Leftrightarrow & -15x \color{red}{-15} & = &16 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -15x+x& = &16+15 \\\Leftrightarrow & -14x& = &31 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{31}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-31}{14} & & \\ & V = \left\{ \frac{-31}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+6)& = & -3 \color{red}{-} (-15+x) \\\Leftrightarrow & -16x+24& = &-3+15-x \\\Leftrightarrow & -16x \color{red}{+24} & = &12 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -16x+x& = &12-24 \\\Leftrightarrow & -15x& = &-12 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-12}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-3)& = & 12 \color{red}{-} (-5+x) \\\Leftrightarrow & 36x-18& = &12+5-x \\\Leftrightarrow & 36x \color{red}{-18} & = &17 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 36x+x& = &17+18 \\\Leftrightarrow & 37x& = &35 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{35}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{35}{37} & & \\ & V = \left\{ \frac{35}{37} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+7)& = & 11 \color{red}{-} (-11+x) \\\Leftrightarrow & 20x+28& = &11+11-x \\\Leftrightarrow & 20x \color{red}{+28} & = &22 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 20x+x& = &22-28 \\\Leftrightarrow & 21x& = &-6 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-6}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x+4)& = & -15 \color{red}{+} (4+x) \\\Leftrightarrow & -12x+12& = &-15+4+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-11-12 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x-1)& = & -12 \color{red}{+} (10+x) \\\Leftrightarrow & -2x-2& = &-12+10+x \\\Leftrightarrow & -2x \color{red}{-2} & = &-2 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -2x-x& = &-2+2 \\\Leftrightarrow & -3x& = &0 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{0}{ \color{red}{-3} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+6)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & -30x+30& = &-7-12+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-19 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-19-30 \\\Leftrightarrow & -31x& = &-49 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-49}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{49}{31} & & \\ & V = \left\{ \frac{49}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-4)& = & -4 \color{red}{+} (3+4x) \\\Leftrightarrow & -15x-12& = &-4+3+4x \\\Leftrightarrow & -15x \color{red}{-12} & = &-1 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & -15x-4x& = &-1+12 \\\Leftrightarrow & -19x& = &11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x-1)& = & 1 \color{red}{+} (7+4x) \\\Leftrightarrow & -15x-3& = &1+7+4x \\\Leftrightarrow & -15x \color{red}{-3} & = &8 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & -15x-4x& = &8+3 \\\Leftrightarrow & -19x& = &11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x+2)& = & -9 \color{red}{-} (12+x) \\\Leftrightarrow & 12x+8& = &-9-12-x \\\Leftrightarrow & 12x \color{red}{+8} & = &-21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &-21-8 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x-7)& = & -7 \color{red}{+} (12+x) \\\Leftrightarrow & -12x-28& = &-7+12+x \\\Leftrightarrow & -12x \color{red}{-28} & = &5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -12x-x& = &5+28 \\\Leftrightarrow & -13x& = &33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-33}{13} & & \\ & V = \left\{ \frac{-33}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-1)& = & 5 \color{red}{-} (1+x) \\\Leftrightarrow & 2x-2& = &5-1-x \\\Leftrightarrow & 2x \color{red}{-2} & = &4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 2x+x& = &4+2 \\\Leftrightarrow & 3x& = &6 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{6}{ \color{red}{3} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)