Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-5)& = & -10 \color{red}{+} (13+x) \\\Leftrightarrow & 16x-20& = &-10+13+x \\\Leftrightarrow & 16x \color{red}{-20} & = &3 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 16x-x& = &3+20 \\\Leftrightarrow & 15x& = &23 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{23}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{23}{15} & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x-7)& = & 6 \color{red}{+} (1+x) \\\Leftrightarrow & 30x-35& = &6+1+x \\\Leftrightarrow & 30x \color{red}{-35} & = &7 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &7+35 \\\Leftrightarrow & 29x& = &42 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{42}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{42}{29} & & \\ & V = \left\{ \frac{42}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+5)& = & 14 \color{red}{-} (-15+x) \\\Leftrightarrow & 30x+30& = &14+15-x \\\Leftrightarrow & 30x \color{red}{+30} & = &29 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &29-30 \\\Leftrightarrow & 31x& = &-1 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-1}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-1}{31} & & \\ & V = \left\{ \frac{-1}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-6)& = & 2 \color{red}{+} (-5-5x) \\\Leftrightarrow & -18x-36& = &2-5-5x \\\Leftrightarrow & -18x \color{red}{-36} & = &-3 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -18x+5x& = &-3+36 \\\Leftrightarrow & -13x& = &33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-33}{13} & & \\ & V = \left\{ \frac{-33}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-4)& = & -7 \color{red}{-} (3+2x) \\\Leftrightarrow & 15x-20& = &-7-3-2x \\\Leftrightarrow & 15x \color{red}{-20} & = &-10 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & 15x+2x& = &-10+20 \\\Leftrightarrow & 17x& = &10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+6)& = & -4 \color{red}{-} (14+4x) \\\Leftrightarrow & -5x+30& = &-4-14-4x \\\Leftrightarrow & -5x \color{red}{+30} & = &-18 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &-18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & -5x+4x& = &-18-30 \\\Leftrightarrow & -x& = &-48 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-48}{ \color{red}{-1} } \\\Leftrightarrow & x = 48 & & \\ & V = \left\{ 48 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-7)& = & 2 \color{red}{+} (-12-3x) \\\Leftrightarrow & 4x-28& = &2-12-3x \\\Leftrightarrow & 4x \color{red}{-28} & = &-10 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 4x+3x& = &-10+28 \\\Leftrightarrow & 7x& = &18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x-4)& = & 11 \color{red}{-} (13+x) \\\Leftrightarrow & 18x-12& = &11-13-x \\\Leftrightarrow & 18x \color{red}{-12} & = &-2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &-2+12 \\\Leftrightarrow & 19x& = &10 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{10}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{10}{19} & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x-3)& = & 10 \color{red}{+} (-15-5x) \\\Leftrightarrow & 36x-18& = &10-15-5x \\\Leftrightarrow & 36x \color{red}{-18} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 36x+5x& = &-5+18 \\\Leftrightarrow & 41x& = &13 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{13}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{13}{41} & & \\ & V = \left\{ \frac{13}{41} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x+5)& = & 5 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x+30& = &5-4+x \\\Leftrightarrow & -24x \color{red}{+30} & = &1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &1-30 \\\Leftrightarrow & -25x& = &-29 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-29}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x+1)& = & -2 \color{red}{+} (-12+x) \\\Leftrightarrow & 8x+4& = &-2-12+x \\\Leftrightarrow & 8x \color{red}{+4} & = &-14 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 8x-x& = &-14-4 \\\Leftrightarrow & 7x& = &-18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+2)& = & -12 \color{red}{-} (-8+x) \\\Leftrightarrow & -6x+12& = &-12+8-x \\\Leftrightarrow & -6x \color{red}{+12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -6x+x& = &-4-12 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)