Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-7)& = & 4 \color{red}{+} (-11-4x) \\\Leftrightarrow & 5x-35& = &4-11-4x \\\Leftrightarrow & 5x \color{red}{-35} & = &-7 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & 5x+4x& = &-7+35 \\\Leftrightarrow & 9x& = &28 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{28}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{28}{9} & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+2)& = & 11 \color{red}{+} (10+x) \\\Leftrightarrow & -20x+8& = &11+10+x \\\Leftrightarrow & -20x \color{red}{+8} & = &21 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &21-8 \\\Leftrightarrow & -21x& = &13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x+2)& = & -10 \color{red}{-} (11+x) \\\Leftrightarrow & -24x+8& = &-10-11-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-21-8 \\\Leftrightarrow & -23x& = &-29 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-29}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{29}{23} & & \\ & V = \left\{ \frac{29}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x+6)& = & -11 \color{red}{+} (-13+x) \\\Leftrightarrow & -4x+24& = &-11-13+x \\\Leftrightarrow & -4x \color{red}{+24} & = &-24 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -4x-x& = &-24-24 \\\Leftrightarrow & -5x& = &-48 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-48}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{48}{5} & & \\ & V = \left\{ \frac{48}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x+6)& = & -5 \color{red}{+} (-1-5x) \\\Leftrightarrow & 18x+18& = &-5-1-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &-6-18 \\\Leftrightarrow & 23x& = &-24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x+6)& = & -9 \color{red}{-} (15+x) \\\Leftrightarrow & 24x+24& = &-9-15-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-24 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-24-24 \\\Leftrightarrow & 25x& = &-48 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-48}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-48}{25} & & \\ & V = \left\{ \frac{-48}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+5)& = & 7 \color{red}{+} (-6+x) \\\Leftrightarrow & -36x+30& = &7-6+x \\\Leftrightarrow & -36x \color{red}{+30} & = &1 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -36x-x& = &1-30 \\\Leftrightarrow & -37x& = &-29 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-29}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{29}{37} & & \\ & V = \left\{ \frac{29}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+3)& = & 2 \color{red}{-} (7-5x) \\\Leftrightarrow & 18x+9& = &2-7+5x \\\Leftrightarrow & 18x \color{red}{+9} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 18x-5x& = &-5-9 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-2)& = & 10 \color{red}{+} (9+x) \\\Leftrightarrow & -16x-8& = &10+9+x \\\Leftrightarrow & -16x \color{red}{-8} & = &19 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -16x-x& = &19+8 \\\Leftrightarrow & -17x& = &27 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{27}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-27}{17} & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+3)& = & 8 \color{red}{-} (-1+x) \\\Leftrightarrow & 30x+15& = &8+1-x \\\Leftrightarrow & 30x \color{red}{+15} & = &9 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 30x+x& = &9-15 \\\Leftrightarrow & 31x& = &-6 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-6}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-6}{31} & & \\ & V = \left\{ \frac{-6}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-2)& = & 4 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x-8& = &4+11-x \\\Leftrightarrow & -24x \color{red}{-8} & = &15 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &15+8 \\\Leftrightarrow & -23x& = &23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{23}{ \color{red}{-23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-6)& = & 6 \color{red}{+} (4+x) \\\Leftrightarrow & -9x-18& = &6+4+x \\\Leftrightarrow & -9x \color{red}{-18} & = &10 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -9x-x& = &10+18 \\\Leftrightarrow & -10x& = &28 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{28}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)