Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-7)& = & -6 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-42& = &-6-14-x \\\Leftrightarrow & -12x \color{red}{-42} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -12x+x& = &-20+42 \\\Leftrightarrow & -11x& = &22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{22}{ \color{red}{-11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-5)& = & -5 \color{red}{+} (-5-5x) \\\Leftrightarrow & -8x-20& = &-5-5-5x \\\Leftrightarrow & -8x \color{red}{-20} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+20} \\\Leftrightarrow & -8x+5x& = &-10+20 \\\Leftrightarrow & -3x& = &10 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{10}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-2)& = & 1 \color{red}{+} (-13-4x) \\\Leftrightarrow & 25x-10& = &1-13-4x \\\Leftrightarrow & 25x \color{red}{-10} & = &-12 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &-12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & 25x+4x& = &-12+10 \\\Leftrightarrow & 29x& = &-2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-6)& = & -7 \color{red}{+} (-12-3x) \\\Leftrightarrow & -4x-12& = &-7-12-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &-19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &-19+12 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x+6)& = & 15 \color{red}{+} (15-5x) \\\Leftrightarrow & 16x+24& = &15+15-5x \\\Leftrightarrow & 16x \color{red}{+24} & = &30 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &30 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 16x+5x& = &30-24 \\\Leftrightarrow & 21x& = &6 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{6}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-5)& = & -10 \color{red}{-} (-8+x) \\\Leftrightarrow & 4x-10& = &-10+8-x \\\Leftrightarrow & 4x \color{red}{-10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 4x+x& = &-2+10 \\\Leftrightarrow & 5x& = &8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x+4)& = & 4 \color{red}{-} (13+x) \\\Leftrightarrow & 18x+24& = &4-13-x \\\Leftrightarrow & 18x \color{red}{+24} & = &-9 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 18x+x& = &-9-24 \\\Leftrightarrow & 19x& = &-33 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-33}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-33}{19} & & \\ & V = \left\{ \frac{-33}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x-7)& = & 13 \color{red}{+} (-11-5x) \\\Leftrightarrow & -18x-42& = &13-11-5x \\\Leftrightarrow & -18x \color{red}{-42} & = &2 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & -18x+5x& = &2+42 \\\Leftrightarrow & -13x& = &44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-44}{13} & & \\ & V = \left\{ \frac{-44}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+2)& = & 12 \color{red}{+} (4+4x) \\\Leftrightarrow & 9x+6& = &12+4+4x \\\Leftrightarrow & 9x \color{red}{+6} & = &16 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & 9x-4x& = &16-6 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-4)& = & 6 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-12& = &6+4+x \\\Leftrightarrow & 12x \color{red}{-12} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &10+12 \\\Leftrightarrow & 11x& = &22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{22}{ \color{red}{11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x-2)& = & -7 \color{red}{+} (13-5x) \\\Leftrightarrow & -18x-12& = &-7+13-5x \\\Leftrightarrow & -18x \color{red}{-12} & = &6 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -18x+5x& = &6+12 \\\Leftrightarrow & -13x& = &18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-6x+2)& = & 13 \color{red}{+} (-5-5x) \\\Leftrightarrow & -18x+6& = &13-5-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &8 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &8-6 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)