Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x-7)& = & -6 \color{red}{+} (3+3x) \\\Leftrightarrow & -4x-14& = &-6+3+3x \\\Leftrightarrow & -4x \color{red}{-14} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -4x-3x& = &-3+14 \\\Leftrightarrow & -7x& = &11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x-1)& = & -13 \color{red}{-} (-1+x) \\\Leftrightarrow & 24x-4& = &-13+1-x \\\Leftrightarrow & 24x \color{red}{-4} & = &-12 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &-12+4 \\\Leftrightarrow & 25x& = &-8 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-8}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-2)& = & -6 \color{red}{+} (7-3x) \\\Leftrightarrow & 4x-4& = &-6+7-3x \\\Leftrightarrow & 4x \color{red}{-4} & = &1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 4x+3x& = &1+4 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+3)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & -30x+15& = &-15+6+x \\\Leftrightarrow & -30x \color{red}{+15} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -30x-x& = &-9-15 \\\Leftrightarrow & -31x& = &-24 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-24}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x-7)& = & 15 \color{red}{+} (15-2x) \\\Leftrightarrow & -15x-35& = &15+15-2x \\\Leftrightarrow & -15x \color{red}{-35} & = &30 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &30 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -15x+2x& = &30+35 \\\Leftrightarrow & -13x& = &65 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{65}{ \color{red}{-13} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-5)& = & -9 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x-30& = &-9-6+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-15+30 \\\Leftrightarrow & 29x& = &15 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{15}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{15}{29} & & \\ & V = \left\{ \frac{15}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x-2)& = & -9 \color{red}{+} (8+3x) \\\Leftrightarrow & -16x-8& = &-9+8+3x \\\Leftrightarrow & -16x \color{red}{-8} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -16x-3x& = &-1+8 \\\Leftrightarrow & -19x& = &7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-7}{19} & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x+1)& = & 15 \color{red}{+} (-12+x) \\\Leftrightarrow & -6x+2& = &15-12+x \\\Leftrightarrow & -6x \color{red}{+2} & = &3 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -6x-x& = &3-2 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+6)& = & -11 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+24& = &-11+10+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-1-24 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+5)& = & 8 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x+20& = &8-7+x \\\Leftrightarrow & 20x \color{red}{+20} & = &1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &1-20 \\\Leftrightarrow & 19x& = &-19 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-19}{ \color{red}{19} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x-6)& = & 6 \color{red}{-} (1+x) \\\Leftrightarrow & 24x-36& = &6-1-x \\\Leftrightarrow & 24x \color{red}{-36} & = &5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &5+36 \\\Leftrightarrow & 25x& = &41 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{41}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{41}{25} & & \\ & V = \left\{ \frac{41}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-5)& = & 3 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x-30& = &3-8+x \\\Leftrightarrow & 24x \color{red}{-30} & = &-5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 24x-x& = &-5+30 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)