Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x-1)& = & 13 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x-5& = &13-4+x \\\Leftrightarrow & -30x \color{red}{-5} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &9+5 \\\Leftrightarrow & -31x& = &14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x+7)& = & 8 \color{red}{+} (7+3x) \\\Leftrightarrow & -2x+14& = &8+7+3x \\\Leftrightarrow & -2x \color{red}{+14} & = &15 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -2x-3x& = &15-14 \\\Leftrightarrow & -5x& = &1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+1)& = & -6 \color{red}{+} (-2-5x) \\\Leftrightarrow & -8x+4& = &-6-2-5x \\\Leftrightarrow & -8x \color{red}{+4} & = &-8 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & -8x+5x& = &-8-4 \\\Leftrightarrow & -3x& = &-12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-12}{ \color{red}{-3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+6)& = & -14 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x+12& = &-14-11+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-25-12 \\\Leftrightarrow & 11x& = &-37 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-37}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-37}{11} & & \\ & V = \left\{ \frac{-37}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-7)& = & -12 \color{red}{+} (8+4x) \\\Leftrightarrow & 3x-21& = &-12+8+4x \\\Leftrightarrow & 3x \color{red}{-21} & = &-4 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &-4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & 3x-4x& = &-4+21 \\\Leftrightarrow & -x& = &17 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{17}{ \color{red}{-1} } \\\Leftrightarrow & x = -17 & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x+5)& = & 15 \color{red}{-} (2-5x) \\\Leftrightarrow & 18x+15& = &15-2+5x \\\Leftrightarrow & 18x \color{red}{+15} & = &13 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & 18x-5x& = &13-15 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+1)& = & -6 \color{red}{-} (6+x) \\\Leftrightarrow & -20x+5& = &-6-6-x \\\Leftrightarrow & -20x \color{red}{+5} & = &-12 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -20x+x& = &-12-5 \\\Leftrightarrow & -19x& = &-17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-7)& = & 8 \color{red}{-} (-2+x) \\\Leftrightarrow & -24x-42& = &8+2-x \\\Leftrightarrow & -24x \color{red}{-42} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &10+42 \\\Leftrightarrow & -23x& = &52 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{52}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-52}{23} & & \\ & V = \left\{ \frac{-52}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x-4)& = & -2 \color{red}{+} (-1-3x) \\\Leftrightarrow & -10x-8& = &-2-1-3x \\\Leftrightarrow & -10x \color{red}{-8} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -10x+3x& = &-3+8 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+2)& = & 2 \color{red}{-} (7-3x) \\\Leftrightarrow & -25x+10& = &2-7+3x \\\Leftrightarrow & -25x \color{red}{+10} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -25x-3x& = &-5-10 \\\Leftrightarrow & -28x& = &-15 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-15}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{15}{28} & & \\ & V = \left\{ \frac{15}{28} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-2)& = & -3 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x-12& = &-3-5+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-8+12 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-4)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x-20& = &-13-4+x \\\Leftrightarrow & -20x \color{red}{-20} & = &-17 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &-17+20 \\\Leftrightarrow & -21x& = &3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)