Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+4)& = & -11 \color{red}{+} (13+x) \\\Leftrightarrow & -30x+24& = &-11+13+x \\\Leftrightarrow & -30x \color{red}{+24} & = &2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &2-24 \\\Leftrightarrow & -31x& = &-22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x-1)& = & -8 \color{red}{+} (-9-5x) \\\Leftrightarrow & 6x-2& = &-8-9-5x \\\Leftrightarrow & 6x \color{red}{-2} & = &-17 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+2} \\\Leftrightarrow & 6x+5x& = &-17+2 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-7)& = & 1 \color{red}{+} (-12+x) \\\Leftrightarrow & -24x-28& = &1-12+x \\\Leftrightarrow & -24x \color{red}{-28} & = &-11 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -24x-x& = &-11+28 \\\Leftrightarrow & -25x& = &17 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{17}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x+6)& = & -14 \color{red}{+} (3-4x) \\\Leftrightarrow & -25x+30& = &-14+3-4x \\\Leftrightarrow & -25x \color{red}{+30} & = &-11 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & -25x+4x& = &-11-30 \\\Leftrightarrow & -21x& = &-41 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-41}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{41}{21} & & \\ & V = \left\{ \frac{41}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x-5)& = & 9 \color{red}{-} (-6-3x) \\\Leftrightarrow & 10x-10& = &9+6+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &15 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &15+10 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+5)& = & 10 \color{red}{+} (-12+x) \\\Leftrightarrow & 4x+10& = &10-12+x \\\Leftrightarrow & 4x \color{red}{+10} & = &-2 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 4x-x& = &-2-10 \\\Leftrightarrow & 3x& = &-12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-12}{ \color{red}{3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-3)& = & 12 \color{red}{-} (10+x) \\\Leftrightarrow & 18x-18& = &12-10-x \\\Leftrightarrow & 18x \color{red}{-18} & = &2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 18x+x& = &2+18 \\\Leftrightarrow & 19x& = &20 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{20}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{20}{19} & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x-4)& = & -5 \color{red}{+} (-5-5x) \\\Leftrightarrow & 16x-16& = &-5-5-5x \\\Leftrightarrow & 16x \color{red}{-16} & = &-10 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+16} \\\Leftrightarrow & 16x+5x& = &-10+16 \\\Leftrightarrow & 21x& = &6 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{6}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-2)& = & -3 \color{red}{-} (-3+x) \\\Leftrightarrow & -3x-6& = &-3+3-x \\\Leftrightarrow & -3x \color{red}{-6} & = &0 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -3x+x& = &0+6 \\\Leftrightarrow & -2x& = &6 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{6}{ \color{red}{-2} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-6)& = & -7 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x-36& = &-7+4-x \\\Leftrightarrow & 24x \color{red}{-36} & = &-3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &-3+36 \\\Leftrightarrow & 25x& = &33 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{33}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x-2)& = & 4 \color{red}{-} (10+4x) \\\Leftrightarrow & -15x-6& = &4-10-4x \\\Leftrightarrow & -15x \color{red}{-6} & = &-6 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -15x+4x& = &-6+6 \\\Leftrightarrow & -11x& = &0 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{0}{ \color{red}{-11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+6)& = & -5 \color{red}{-} (14+x) \\\Leftrightarrow & -20x+24& = &-5-14-x \\\Leftrightarrow & -20x \color{red}{+24} & = &-19 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -20x+x& = &-19-24 \\\Leftrightarrow & -19x& = &-43 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-43}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{43}{19} & & \\ & V = \left\{ \frac{43}{19} \right\} & \\\end{align}\)