Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+7)& = & 6 \color{red}{+} (-4+4x) \\\Leftrightarrow & -3x+21& = &6-4+4x \\\Leftrightarrow & -3x \color{red}{+21} & = &2 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & -3x-4x& = &2-21 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x+6)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & -20x+30& = &-9-9-x \\\Leftrightarrow & -20x \color{red}{+30} & = &-18 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -20x+x& = &-18-30 \\\Leftrightarrow & -19x& = &-48 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-48}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{48}{19} & & \\ & V = \left\{ \frac{48}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-6)& = & 3 \color{red}{-} (8+3x) \\\Leftrightarrow & -20x-30& = &3-8-3x \\\Leftrightarrow & -20x \color{red}{-30} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & -20x+3x& = &-5+30 \\\Leftrightarrow & -17x& = &25 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{25}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-25}{17} & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x+7)& = & -4 \color{red}{-} (-12-3x) \\\Leftrightarrow & 16x+28& = &-4+12+3x \\\Leftrightarrow & 16x \color{red}{+28} & = &8 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 16x-3x& = &8-28 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+6)& = & -2 \color{red}{-} (-13+x) \\\Leftrightarrow & -20x+24& = &-2+13-x \\\Leftrightarrow & -20x \color{red}{+24} & = &11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -20x+x& = &11-24 \\\Leftrightarrow & -19x& = &-13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-1)& = & -11 \color{red}{-} (9+x) \\\Leftrightarrow & 8x-4& = &-11-9-x \\\Leftrightarrow & 8x \color{red}{-4} & = &-20 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &-20+4 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-3)& = & -1 \color{red}{-} (13+4x) \\\Leftrightarrow & 3x-9& = &-1-13-4x \\\Leftrightarrow & 3x \color{red}{-9} & = &-14 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &-14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & 3x+4x& = &-14+9 \\\Leftrightarrow & 7x& = &-5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x-7)& = & 9 \color{red}{-} (-2+4x) \\\Leftrightarrow & 9x-21& = &9+2-4x \\\Leftrightarrow & 9x \color{red}{-21} & = &11 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 9x+4x& = &11+21 \\\Leftrightarrow & 13x& = &32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x+5)& = & -15 \color{red}{-} (15+x) \\\Leftrightarrow & 2x+10& = &-15-15-x \\\Leftrightarrow & 2x \color{red}{+10} & = &-30 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-30 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 2x+x& = &-30-10 \\\Leftrightarrow & 3x& = &-40 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-40}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-40}{3} & & \\ & V = \left\{ \frac{-40}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x+3)& = & 9 \color{red}{-} (2+x) \\\Leftrightarrow & -18x+18& = &9-2-x \\\Leftrightarrow & -18x \color{red}{+18} & = &7 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -18x+x& = &7-18 \\\Leftrightarrow & -17x& = &-11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x-5)& = & 11 \color{red}{-} (-8+x) \\\Leftrightarrow & -30x-25& = &11+8-x \\\Leftrightarrow & -30x \color{red}{-25} & = &19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -30x+x& = &19+25 \\\Leftrightarrow & -29x& = &44 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{44}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-44}{29} & & \\ & V = \left\{ \frac{-44}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-7)& = & -15 \color{red}{-} (6+x) \\\Leftrightarrow & 30x-42& = &-15-6-x \\\Leftrightarrow & 30x \color{red}{-42} & = &-21 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 30x+x& = &-21+42 \\\Leftrightarrow & 31x& = &21 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{21}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{21}{31} & & \\ & V = \left\{ \frac{21}{31} \right\} & \\\end{align}\)