Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+2)& = & 11 \color{red}{+} (-9+4x) \\\Leftrightarrow & 9x+6& = &11-9+4x \\\Leftrightarrow & 9x \color{red}{+6} & = &2 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & 9x-4x& = &2-6 \\\Leftrightarrow & 5x& = &-4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x+4)& = & -12 \color{red}{+} (10+4x) \\\Leftrightarrow & -15x+12& = &-12+10+4x \\\Leftrightarrow & -15x \color{red}{+12} & = &-2 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & -15x-4x& = &-2-12 \\\Leftrightarrow & -19x& = &-14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+6)& = & 1 \color{red}{+} (14+3x) \\\Leftrightarrow & 4x+12& = &1+14+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &15 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &15-12 \\\Leftrightarrow & x& = &3 \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-6)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & -8x-12& = &-4+8-x \\\Leftrightarrow & -8x \color{red}{-12} & = &4 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &4+12 \\\Leftrightarrow & -7x& = &16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x-6)& = & -13 \color{red}{+} (15+x) \\\Leftrightarrow & 20x-24& = &-13+15+x \\\Leftrightarrow & 20x \color{red}{-24} & = &2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &2+24 \\\Leftrightarrow & 19x& = &26 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{26}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{26}{19} & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-1)& = & -15 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x-4& = &-15+9-x \\\Leftrightarrow & 24x \color{red}{-4} & = &-6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &-6+4 \\\Leftrightarrow & 25x& = &-2 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-2}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-2}{25} & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x-4)& = & 8 \color{red}{-} (-3+x) \\\Leftrightarrow & 16x-16& = &8+3-x \\\Leftrightarrow & 16x \color{red}{-16} & = &11 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 16x+x& = &11+16 \\\Leftrightarrow & 17x& = &27 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{27}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{27}{17} & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x-3)& = & 9 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x-18& = &9-14+x \\\Leftrightarrow & -12x \color{red}{-18} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &-5+18 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-6)& = & 12 \color{red}{-} (-3+3x) \\\Leftrightarrow & -4x-24& = &12+3-3x \\\Leftrightarrow & -4x \color{red}{-24} & = &15 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -4x+3x& = &15+24 \\\Leftrightarrow & -x& = &39 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{39}{ \color{red}{-1} } \\\Leftrightarrow & x = -39 & & \\ & V = \left\{ -39 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x+2)& = & 6 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+12& = &6-12+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-6-12 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-6)& = & 15 \color{red}{+} (9+x) \\\Leftrightarrow & -12x-18& = &15+9+x \\\Leftrightarrow & -12x \color{red}{-18} & = &24 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &24+18 \\\Leftrightarrow & -13x& = &42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-42}{13} & & \\ & V = \left\{ \frac{-42}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+6)& = & -8 \color{red}{+} (-2+x) \\\Leftrightarrow & -30x+30& = &-8-2+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-10-30 \\\Leftrightarrow & -31x& = &-40 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-40}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{40}{31} & & \\ & V = \left\{ \frac{40}{31} \right\} & \\\end{align}\)