Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x+5)& = & -6 \color{red}{-} (4+x) \\\Leftrightarrow & -24x+30& = &-6-4-x \\\Leftrightarrow & -24x \color{red}{+30} & = &-10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -24x+x& = &-10-30 \\\Leftrightarrow & -23x& = &-40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{40}{23} & & \\ & V = \left\{ \frac{40}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-7)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & 36x-42& = &-7-1+x \\\Leftrightarrow & 36x \color{red}{-42} & = &-8 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 36x-x& = &-8+42 \\\Leftrightarrow & 35x& = &34 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{34}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{34}{35} & & \\ & V = \left\{ \frac{34}{35} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-4)& = & 3 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x-16& = &3-8+x \\\Leftrightarrow & -24x \color{red}{-16} & = &-5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -24x-x& = &-5+16 \\\Leftrightarrow & -25x& = &11 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{11}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-11}{25} & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+1)& = & -9 \color{red}{+} (9+x) \\\Leftrightarrow & -30x+5& = &-9+9+x \\\Leftrightarrow & -30x \color{red}{+5} & = &0 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -30x-x& = &0-5 \\\Leftrightarrow & -31x& = &-5 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-5}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{5}{31} & & \\ & V = \left\{ \frac{5}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (2x-3)& = & 2 \color{red}{+} (14+3x) \\\Leftrightarrow & 8x-12& = &2+14+3x \\\Leftrightarrow & 8x \color{red}{-12} & = &16 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 8x-3x& = &16+12 \\\Leftrightarrow & 5x& = &28 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{28}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{28}{5} & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-5)& = & 2 \color{red}{-} (-14-5x) \\\Leftrightarrow & -36x-30& = &2+14+5x \\\Leftrightarrow & -36x \color{red}{-30} & = &16 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -36x-5x& = &16+30 \\\Leftrightarrow & -41x& = &46 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{46}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-46}{41} & & \\ & V = \left\{ \frac{-46}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-2)& = & -15 \color{red}{-} (-3-2x) \\\Leftrightarrow & -3x-6& = &-15+3+2x \\\Leftrightarrow & -3x \color{red}{-6} & = &-12 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -3x-2x& = &-12+6 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x-2)& = & 11 \color{red}{+} (2+x) \\\Leftrightarrow & -30x-10& = &11+2+x \\\Leftrightarrow & -30x \color{red}{-10} & = &13 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -30x-x& = &13+10 \\\Leftrightarrow & -31x& = &23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-23}{31} & & \\ & V = \left\{ \frac{-23}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x-3)& = & 14 \color{red}{+} (4+x) \\\Leftrightarrow & -24x-18& = &14+4+x \\\Leftrightarrow & -24x \color{red}{-18} & = &18 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &18+18 \\\Leftrightarrow & -25x& = &36 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{36}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-36}{25} & & \\ & V = \left\{ \frac{-36}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x-3)& = & 7 \color{red}{+} (-4-5x) \\\Leftrightarrow & -18x-9& = &7-4-5x \\\Leftrightarrow & -18x \color{red}{-9} & = &3 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & -18x+5x& = &3+9 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+6)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x+24& = &8-4+x \\\Leftrightarrow & -20x \color{red}{+24} & = &4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &4-24 \\\Leftrightarrow & -21x& = &-20 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-20}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-1)& = & -10 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-6& = &-10+14-x \\\Leftrightarrow & 30x \color{red}{-6} & = &4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &4+6 \\\Leftrightarrow & 31x& = &10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)