Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x-2)& = & -12 \color{red}{-} (-7+3x) \\\Leftrightarrow & -4x-4& = &-12+7-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &-5+4 \\\Leftrightarrow & -x& = &-1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-1}{ \color{red}{-1} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+7)& = & -14 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+28& = &-14+10-x \\\Leftrightarrow & -12x \color{red}{+28} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &-4-28 \\\Leftrightarrow & -11x& = &-32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+4)& = & 4 \color{red}{+} (6+x) \\\Leftrightarrow & -18x+12& = &4+6+x \\\Leftrightarrow & -18x \color{red}{+12} & = &10 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &10-12 \\\Leftrightarrow & -19x& = &-2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-6)& = & 14 \color{red}{-} (-6-3x) \\\Leftrightarrow & 16x-24& = &14+6+3x \\\Leftrightarrow & 16x \color{red}{-24} & = &20 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 16x-3x& = &20+24 \\\Leftrightarrow & 13x& = &44 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{44}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{44}{13} & & \\ & V = \left\{ \frac{44}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-2)& = & -12 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x-12& = &-12+15-x \\\Leftrightarrow & 12x \color{red}{-12} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &3+12 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x+5)& = & -13 \color{red}{-} (12-2x) \\\Leftrightarrow & -15x+15& = &-13-12+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &-25 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-25 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &-25-15 \\\Leftrightarrow & -17x& = &-40 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-40}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{40}{17} & & \\ & V = \left\{ \frac{40}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+5)& = & 7 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x+30& = &7+9-x \\\Leftrightarrow & 30x \color{red}{+30} & = &16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &16-30 \\\Leftrightarrow & 31x& = &-14 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-14}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-6)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & -36x-36& = &9+7-x \\\Leftrightarrow & -36x \color{red}{-36} & = &16 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -36x+x& = &16+36 \\\Leftrightarrow & -35x& = &52 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{52}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-52}{35} & & \\ & V = \left\{ \frac{-52}{35} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x+4)& = & 7 \color{red}{+} (-4+x) \\\Leftrightarrow & 30x+20& = &7-4+x \\\Leftrightarrow & 30x \color{red}{+20} & = &3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &3-20 \\\Leftrightarrow & 29x& = &-17 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-17}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-17}{29} & & \\ & V = \left\{ \frac{-17}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x-2)& = & -12 \color{red}{+} (-12+3x) \\\Leftrightarrow & 8x-4& = &-12-12+3x \\\Leftrightarrow & 8x \color{red}{-4} & = &-24 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 8x-3x& = &-24+4 \\\Leftrightarrow & 5x& = &-20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-20}{ \color{red}{5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x+3)& = & 7 \color{red}{-} (10-5x) \\\Leftrightarrow & -16x+12& = &7-10+5x \\\Leftrightarrow & -16x \color{red}{+12} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -16x-5x& = &-3-12 \\\Leftrightarrow & -21x& = &-15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x-4)& = & 6 \color{red}{+} (-6-2x) \\\Leftrightarrow & 15x-12& = &6-6-2x \\\Leftrightarrow & 15x \color{red}{-12} & = &0 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & 15x+2x& = &0+12 \\\Leftrightarrow & 17x& = &12 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{12}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)