Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+1)& = & 12 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x+2& = &12+12-x \\\Leftrightarrow & 12x \color{red}{+2} & = &24 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 12x+x& = &24-2 \\\Leftrightarrow & 13x& = &22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+2)& = & -15 \color{red}{-} (12+x) \\\Leftrightarrow & -20x+8& = &-15-12-x \\\Leftrightarrow & -20x \color{red}{+8} & = &-27 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -20x+x& = &-27-8 \\\Leftrightarrow & -19x& = &-35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-7)& = & 12 \color{red}{+} (3+3x) \\\Leftrightarrow & 5x-35& = &12+3+3x \\\Leftrightarrow & 5x \color{red}{-35} & = &15 \color{red}{+3x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 5x-3x& = &15+35 \\\Leftrightarrow & 2x& = &50 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{50}{ \color{red}{2} } \\\Leftrightarrow & x = 25 & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x-7)& = & 12 \color{red}{-} (-2-4x) \\\Leftrightarrow & -9x-21& = &12+2+4x \\\Leftrightarrow & -9x \color{red}{-21} & = &14 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & -9x-4x& = &14+21 \\\Leftrightarrow & -13x& = &35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-35}{13} & & \\ & V = \left\{ \frac{-35}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x+3)& = & 5 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x+9& = &5-15-5x \\\Leftrightarrow & -6x \color{red}{+9} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -6x+5x& = &-10-9 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-5)& = & 9 \color{red}{-} (-5-2x) \\\Leftrightarrow & -9x-15& = &9+5+2x \\\Leftrightarrow & -9x \color{red}{-15} & = &14 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -9x-2x& = &14+15 \\\Leftrightarrow & -11x& = &29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x+3)& = & 2 \color{red}{+} (3+x) \\\Leftrightarrow & -16x+12& = &2+3+x \\\Leftrightarrow & -16x \color{red}{+12} & = &5 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -16x-x& = &5-12 \\\Leftrightarrow & -17x& = &-7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-4)& = & 13 \color{red}{-} (-5-5x) \\\Leftrightarrow & 6x-24& = &13+5+5x \\\Leftrightarrow & 6x \color{red}{-24} & = &18 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 6x-5x& = &18+24 \\\Leftrightarrow & x& = &42 \\ & V = \left\{ 42 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x-2)& = & 2 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x-10& = &2+12-x \\\Leftrightarrow & 30x \color{red}{-10} & = &14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &14+10 \\\Leftrightarrow & 31x& = &24 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{24}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x-1)& = & 7 \color{red}{-} (10+3x) \\\Leftrightarrow & 5x-5& = &7-10-3x \\\Leftrightarrow & 5x \color{red}{-5} & = &-3 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 5x+3x& = &-3+5 \\\Leftrightarrow & 8x& = &2 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{2}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+7)& = & -4 \color{red}{+} (6-3x) \\\Leftrightarrow & -4x+14& = &-4+6-3x \\\Leftrightarrow & -4x \color{red}{+14} & = &2 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -4x+3x& = &2-14 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+6)& = & 15 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+18& = &15-4-x \\\Leftrightarrow & -12x \color{red}{+18} & = &11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &11-18 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)