Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+2)& = & -4 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x+6& = &-4-4+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-8-6 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x-1)& = & -15 \color{red}{-} (4-2x) \\\Leftrightarrow & -15x-3& = &-15-4+2x \\\Leftrightarrow & -15x \color{red}{-3} & = &-19 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &-19 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & -15x-2x& = &-19+3 \\\Leftrightarrow & -17x& = &-16 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-16}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{16}{17} & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-4)& = & 10 \color{red}{+} (-10-5x) \\\Leftrightarrow & 18x-24& = &10-10-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &0 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &0+24 \\\Leftrightarrow & 23x& = &24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+6)& = & -8 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+12& = &-8+5-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-3-12 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+7)& = & 10 \color{red}{-} (-9-3x) \\\Leftrightarrow & 4x+28& = &10+9+3x \\\Leftrightarrow & 4x \color{red}{+28} & = &19 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 4x-3x& = &19-28 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+3)& = & -14 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+12& = &-14+6+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-8-12 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-5)& = & 12 \color{red}{-} (-1+x) \\\Leftrightarrow & -18x-30& = &12+1-x \\\Leftrightarrow & -18x \color{red}{-30} & = &13 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -18x+x& = &13+30 \\\Leftrightarrow & -17x& = &43 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{43}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-43}{17} & & \\ & V = \left\{ \frac{-43}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x-1)& = & 3 \color{red}{-} (-12+4x) \\\Leftrightarrow & 15x-3& = &3+12-4x \\\Leftrightarrow & 15x \color{red}{-3} & = &15 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & 15x+4x& = &15+3 \\\Leftrightarrow & 19x& = &18 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{18}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+3)& = & -5 \color{red}{+} (-5+x) \\\Leftrightarrow & -20x+15& = &-5-5+x \\\Leftrightarrow & -20x \color{red}{+15} & = &-10 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -20x-x& = &-10-15 \\\Leftrightarrow & -21x& = &-25 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-25}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{25}{21} & & \\ & V = \left\{ \frac{25}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+7)& = & -13 \color{red}{-} (9+x) \\\Leftrightarrow & -25x+35& = &-13-9-x \\\Leftrightarrow & -25x \color{red}{+35} & = &-22 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -25x+x& = &-22-35 \\\Leftrightarrow & -24x& = &-57 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-57}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{19}{8} & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x+2)& = & -6 \color{red}{-} (-9-4x) \\\Leftrightarrow & 5x+10& = &-6+9+4x \\\Leftrightarrow & 5x \color{red}{+10} & = &3 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & 5x-4x& = &3-10 \\\Leftrightarrow & x& = &-7 \\ & V = \left\{ -7 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+3)& = & 15 \color{red}{-} (-2+4x) \\\Leftrightarrow & 15x+9& = &15+2-4x \\\Leftrightarrow & 15x \color{red}{+9} & = &17 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-9} \\\Leftrightarrow & 15x+4x& = &17-9 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)