Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x-6)& = & -12 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-24& = &-12-12+x \\\Leftrightarrow & 12x \color{red}{-24} & = &-24 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &-24+24 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x-5)& = & 12 \color{red}{+} (11+x) \\\Leftrightarrow & -4x-10& = &12+11+x \\\Leftrightarrow & -4x \color{red}{-10} & = &23 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &23+10 \\\Leftrightarrow & -5x& = &33 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{33}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-33}{5} & & \\ & V = \left\{ \frac{-33}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+3)& = & -13 \color{red}{-} (-5-3x) \\\Leftrightarrow & 16x+12& = &-13+5+3x \\\Leftrightarrow & 16x \color{red}{+12} & = &-8 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 16x-3x& = &-8-12 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (x+6)& = & -7 \color{red}{+} (12-4x) \\\Leftrightarrow & 5x+30& = &-7+12-4x \\\Leftrightarrow & 5x \color{red}{+30} & = &5 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 5x+4x& = &5-30 \\\Leftrightarrow & 9x& = &-25 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-25}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-25}{9} & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x+7)& = & 15 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+14& = &15+4-x \\\Leftrightarrow & -12x \color{red}{+14} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -12x+x& = &19-14 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x-1)& = & 10 \color{red}{-} (13+x) \\\Leftrightarrow & -2x-2& = &10-13-x \\\Leftrightarrow & -2x \color{red}{-2} & = &-3 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -2x+x& = &-3+2 \\\Leftrightarrow & -x& = &-1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-1}{ \color{red}{-1} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-4)& = & 4 \color{red}{+} (-2+4x) \\\Leftrightarrow & 5x-20& = &4-2+4x \\\Leftrightarrow & 5x \color{red}{-20} & = &2 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 5x-4x& = &2+20 \\\Leftrightarrow & x& = &22 \\ & V = \left\{ 22 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+2)& = & -11 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x+12& = &-11-6+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-17 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-17-12 \\\Leftrightarrow & 23x& = &-29 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-29}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-29}{23} & & \\ & V = \left\{ \frac{-29}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+4)& = & 10 \color{red}{-} (4-3x) \\\Leftrightarrow & -10x+8& = &10-4+3x \\\Leftrightarrow & -10x \color{red}{+8} & = &6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -10x-3x& = &6-8 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-3)& = & -10 \color{red}{-} (-15+x) \\\Leftrightarrow & 24x-18& = &-10+15-x \\\Leftrightarrow & 24x \color{red}{-18} & = &5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 24x+x& = &5+18 \\\Leftrightarrow & 25x& = &23 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{23}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{23}{25} & & \\ & V = \left\{ \frac{23}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-1)& = & -14 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x-3& = &-14+2-5x \\\Leftrightarrow & -18x \color{red}{-3} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -18x+5x& = &-12+3 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+4)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & 30x+20& = &6-7+x \\\Leftrightarrow & 30x \color{red}{+20} & = &-1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &-1-20 \\\Leftrightarrow & 29x& = &-21 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-21}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)