Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-2x+3)=-10+(-12-5x)\)
2. \(5(-3x+3)=-13-(-12+x)\)
3. \(6(5x-4)=-14+(8+x)\)
4. \(2(x+7)=9-(4+x)\)
5. \(5(-6x+5)=-4+(4+x)\)
6. \(5(-3x-2)=3-(-12+x)\)
7. \(6(x+4)=-15-(-7-5x)\)
8. \(4(-4x-1)=14-(13+3x)\)
9. \(6(2x+1)=7+(12+x)\)
10. \(6(-2x+4)=12+(4+x)\)
11. \(5(-4x-3)=-6+(13+x)\)
12. \(4(-2x+3)=2-(11+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+3)& = & -10 \color{red}{+} (-12-5x) \\\Leftrightarrow & -6x+9& = &-10-12-5x \\\Leftrightarrow & -6x \color{red}{+9} & = &-22 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -6x+5x& = &-22-9 \\\Leftrightarrow & -x& = &-31 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-31}{ \color{red}{-1} } \\\Leftrightarrow & x = 31 & & \\ & V = \left\{ 31 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+3)& = & -13 \color{red}{-} (-12+x) \\\Leftrightarrow & -15x+15& = &-13+12-x \\\Leftrightarrow & -15x \color{red}{+15} & = &-1 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -15x+x& = &-1-15 \\\Leftrightarrow & -14x& = &-16 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-16}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x-4)& = & -14 \color{red}{+} (8+x) \\\Leftrightarrow & 30x-24& = &-14+8+x \\\Leftrightarrow & 30x \color{red}{-24} & = &-6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 30x-x& = &-6+24 \\\Leftrightarrow & 29x& = &18 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{18}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{18}{29} & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+7)& = & 9 \color{red}{-} (4+x) \\\Leftrightarrow & 2x+14& = &9-4-x \\\Leftrightarrow & 2x \color{red}{+14} & = &5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &5-14 \\\Leftrightarrow & 3x& = &-9 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-9}{ \color{red}{3} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+5)& = & -4 \color{red}{+} (4+x) \\\Leftrightarrow & -30x+25& = &-4+4+x \\\Leftrightarrow & -30x \color{red}{+25} & = &0 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &0-25 \\\Leftrightarrow & -31x& = &-25 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-25}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{25}{31} & & \\ & V = \left\{ \frac{25}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-2)& = & 3 \color{red}{-} (-12+x) \\\Leftrightarrow & -15x-10& = &3+12-x \\\Leftrightarrow & -15x \color{red}{-10} & = &15 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -15x+x& = &15+10 \\\Leftrightarrow & -14x& = &25 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{25}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-25}{14} & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x+4)& = & -15 \color{red}{-} (-7-5x) \\\Leftrightarrow & 6x+24& = &-15+7+5x \\\Leftrightarrow & 6x \color{red}{+24} & = &-8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 6x-5x& = &-8-24 \\\Leftrightarrow & x& = &-32 \\ & V = \left\{ -32 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x-1)& = & 14 \color{red}{-} (13+3x) \\\Leftrightarrow & -16x-4& = &14-13-3x \\\Leftrightarrow & -16x \color{red}{-4} & = &1 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -16x+3x& = &1+4 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x+1)& = & 7 \color{red}{+} (12+x) \\\Leftrightarrow & 12x+6& = &7+12+x \\\Leftrightarrow & 12x \color{red}{+6} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &19-6 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x+4)& = & 12 \color{red}{+} (4+x) \\\Leftrightarrow & -12x+24& = &12+4+x \\\Leftrightarrow & -12x \color{red}{+24} & = &16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -12x-x& = &16-24 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-3)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & -20x-15& = &-6+13+x \\\Leftrightarrow & -20x \color{red}{-15} & = &7 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -20x-x& = &7+15 \\\Leftrightarrow & -21x& = &22 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{22}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-22}{21} & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x+3)& = & 2 \color{red}{-} (11+x) \\\Leftrightarrow & -8x+12& = &2-11-x \\\Leftrightarrow & -8x \color{red}{+12} & = &-9 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &-9-12 \\\Leftrightarrow & -7x& = &-21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-21}{ \color{red}{-7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)