Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (2x+4)& = & -12 \color{red}{-} (11+x) \\\Leftrightarrow & 10x+20& = &-12-11-x \\\Leftrightarrow & 10x \color{red}{+20} & = &-23 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 10x+x& = &-23-20 \\\Leftrightarrow & 11x& = &-43 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-43}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-43}{11} & & \\ & V = \left\{ \frac{-43}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x-5)& = & -9 \color{red}{-} (-1+x) \\\Leftrightarrow & -2x-10& = &-9+1-x \\\Leftrightarrow & -2x \color{red}{-10} & = &-8 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -2x+x& = &-8+10 \\\Leftrightarrow & -x& = &2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{2}{ \color{red}{-1} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+1)& = & 4 \color{red}{+} (-1+x) \\\Leftrightarrow & -8x+4& = &4-1+x \\\Leftrightarrow & -8x \color{red}{+4} & = &3 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -8x-x& = &3-4 \\\Leftrightarrow & -9x& = &-1 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-1}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+5)& = & -5 \color{red}{+} (7-4x) \\\Leftrightarrow & 9x+15& = &-5+7-4x \\\Leftrightarrow & 9x \color{red}{+15} & = &2 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 9x+4x& = &2-15 \\\Leftrightarrow & 13x& = &-13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-13}{ \color{red}{13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+6)& = & 2 \color{red}{+} (-15+3x) \\\Leftrightarrow & 20x+24& = &2-15+3x \\\Leftrightarrow & 20x \color{red}{+24} & = &-13 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 20x-3x& = &-13-24 \\\Leftrightarrow & 17x& = &-37 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-37}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-37}{17} & & \\ & V = \left\{ \frac{-37}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-4)& = & -13 \color{red}{-} (7+x) \\\Leftrightarrow & 30x-20& = &-13-7-x \\\Leftrightarrow & 30x \color{red}{-20} & = &-20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &-20+20 \\\Leftrightarrow & 31x& = &0 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{0}{ \color{red}{31} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & 8 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x-20& = &8+14-x \\\Leftrightarrow & -30x \color{red}{-20} & = &22 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &22+20 \\\Leftrightarrow & -29x& = &42 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{42}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-42}{29} & & \\ & V = \left\{ \frac{-42}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-4)& = & -6 \color{red}{-} (-8+x) \\\Leftrightarrow & 20x-20& = &-6+8-x \\\Leftrightarrow & 20x \color{red}{-20} & = &2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 20x+x& = &2+20 \\\Leftrightarrow & 21x& = &22 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{22}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{22}{21} & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-1)& = & 7 \color{red}{-} (-3+x) \\\Leftrightarrow & 4x-2& = &7+3-x \\\Leftrightarrow & 4x \color{red}{-2} & = &10 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 4x+x& = &10+2 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x+1)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+6& = &-9-9+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-18-6 \\\Leftrightarrow & 11x& = &-24 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-24}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+6)& = & -12 \color{red}{+} (-2+x) \\\Leftrightarrow & 20x+30& = &-12-2+x \\\Leftrightarrow & 20x \color{red}{+30} & = &-14 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 20x-x& = &-14-30 \\\Leftrightarrow & 19x& = &-44 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-44}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-44}{19} & & \\ & V = \left\{ \frac{-44}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+7)& = & 12 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x+35& = &12+2-x \\\Leftrightarrow & -30x \color{red}{+35} & = &14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -30x+x& = &14-35 \\\Leftrightarrow & -29x& = &-21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{21}{29} & & \\ & V = \left\{ \frac{21}{29} \right\} & \\\end{align}\)