Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x-6)& = & -5 \color{red}{-} (6-3x) \\\Leftrightarrow & -4x-24& = &-5-6+3x \\\Leftrightarrow & -4x \color{red}{-24} & = &-11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -4x-3x& = &-11+24 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+3)& = & 12 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x+12& = &12+4-x \\\Leftrightarrow & 20x \color{red}{+12} & = &16 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 20x+x& = &16-12 \\\Leftrightarrow & 21x& = &4 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{4}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x-2)& = & 9 \color{red}{-} (13+x) \\\Leftrightarrow & 20x-8& = &9-13-x \\\Leftrightarrow & 20x \color{red}{-8} & = &-4 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &-4+8 \\\Leftrightarrow & 21x& = &4 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{4}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x-6)& = & 5 \color{red}{-} (15+x) \\\Leftrightarrow & -20x-24& = &5-15-x \\\Leftrightarrow & -20x \color{red}{-24} & = &-10 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -20x+x& = &-10+24 \\\Leftrightarrow & -19x& = &14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+6)& = & -1 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x+12& = &-1-2+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-3-12 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-3)& = & 11 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-6& = &11-11+x \\\Leftrightarrow & -12x \color{red}{-6} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &0+6 \\\Leftrightarrow & -13x& = &6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x-1)& = & 12 \color{red}{-} (-4+x) \\\Leftrightarrow & -16x-4& = &12+4-x \\\Leftrightarrow & -16x \color{red}{-4} & = &16 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -16x+x& = &16+4 \\\Leftrightarrow & -15x& = &20 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{20}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+5)& = & 15 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x+15& = &15+13-x \\\Leftrightarrow & -12x \color{red}{+15} & = &28 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &28-15 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-7)& = & 14 \color{red}{+} (-3-4x) \\\Leftrightarrow & 5x-35& = &14-3-4x \\\Leftrightarrow & 5x \color{red}{-35} & = &11 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & 5x+4x& = &11+35 \\\Leftrightarrow & 9x& = &46 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{46}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{46}{9} & & \\ & V = \left\{ \frac{46}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-3)& = & 12 \color{red}{-} (-14+x) \\\Leftrightarrow & 24x-12& = &12+14-x \\\Leftrightarrow & 24x \color{red}{-12} & = &26 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &26+12 \\\Leftrightarrow & 25x& = &38 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{38}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{38}{25} & & \\ & V = \left\{ \frac{38}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x+7)& = & -10 \color{red}{+} (-13+x) \\\Leftrightarrow & -18x+21& = &-10-13+x \\\Leftrightarrow & -18x \color{red}{+21} & = &-23 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -18x-x& = &-23-21 \\\Leftrightarrow & -19x& = &-44 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-44}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{44}{19} & & \\ & V = \left\{ \frac{44}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x-5)& = & 13 \color{red}{+} (12-5x) \\\Leftrightarrow & 36x-30& = &13+12-5x \\\Leftrightarrow & 36x \color{red}{-30} & = &25 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 36x+5x& = &25+30 \\\Leftrightarrow & 41x& = &55 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{55}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{55}{41} & & \\ & V = \left\{ \frac{55}{41} \right\} & \\\end{align}\)