Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+6)& = & -1 \color{red}{+} (-9+3x) \\\Leftrightarrow & 8x+24& = &-1-9+3x \\\Leftrightarrow & 8x \color{red}{+24} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 8x-3x& = &-10-24 \\\Leftrightarrow & 5x& = &-34 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-34}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-34}{5} & & \\ & V = \left\{ \frac{-34}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x+4)& = & -6 \color{red}{-} (-7-5x) \\\Leftrightarrow & -36x+24& = &-6+7+5x \\\Leftrightarrow & -36x \color{red}{+24} & = &1 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -36x-5x& = &1-24 \\\Leftrightarrow & -41x& = &-23 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-23}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{23}{41} & & \\ & V = \left\{ \frac{23}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x-1)& = & -9 \color{red}{+} (-1-4x) \\\Leftrightarrow & 9x-3& = &-9-1-4x \\\Leftrightarrow & 9x \color{red}{-3} & = &-10 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & 9x+4x& = &-10+3 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-6)& = & -1 \color{red}{-} (15+x) \\\Leftrightarrow & 8x-12& = &-1-15-x \\\Leftrightarrow & 8x \color{red}{-12} & = &-16 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 8x+x& = &-16+12 \\\Leftrightarrow & 9x& = &-4 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-4}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x+3)& = & -3 \color{red}{-} (1+x) \\\Leftrightarrow & 2x+6& = &-3-1-x \\\Leftrightarrow & 2x \color{red}{+6} & = &-4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 2x+x& = &-4-6 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x+5)& = & 8 \color{red}{-} (-13+x) \\\Leftrightarrow & -25x+25& = &8+13-x \\\Leftrightarrow & -25x \color{red}{+25} & = &21 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -25x+x& = &21-25 \\\Leftrightarrow & -24x& = &-4 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-4}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x-3)& = & -2 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-9& = &-2-8-x \\\Leftrightarrow & 12x \color{red}{-9} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &-10+9 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+1)& = & -13 \color{red}{-} (-12+3x) \\\Leftrightarrow & 16x+4& = &-13+12-3x \\\Leftrightarrow & 16x \color{red}{+4} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 16x+3x& = &-1-4 \\\Leftrightarrow & 19x& = &-5 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-5}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x-3)& = & -10 \color{red}{+} (-15-3x) \\\Leftrightarrow & 10x-15& = &-10-15-3x \\\Leftrightarrow & 10x \color{red}{-15} & = &-25 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &-25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 10x+3x& = &-25+15 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+7)& = & -4 \color{red}{-} (3+x) \\\Leftrightarrow & 20x+28& = &-4-3-x \\\Leftrightarrow & 20x \color{red}{+28} & = &-7 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 20x+x& = &-7-28 \\\Leftrightarrow & 21x& = &-35 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-35}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x+2)& = & 1 \color{red}{-} (1+x) \\\Leftrightarrow & 12x+12& = &1-1-x \\\Leftrightarrow & 12x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &0-12 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+7)& = & 4 \color{red}{-} (14+x) \\\Leftrightarrow & -24x+28& = &4-14-x \\\Leftrightarrow & -24x \color{red}{+28} & = &-10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &-10-28 \\\Leftrightarrow & -23x& = &-38 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-38}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{38}{23} & & \\ & V = \left\{ \frac{38}{23} \right\} & \\\end{align}\)