Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x+2)& = & 12 \color{red}{-} (-5-5x) \\\Leftrightarrow & 36x+12& = &12+5+5x \\\Leftrightarrow & 36x \color{red}{+12} & = &17 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 36x-5x& = &17-12 \\\Leftrightarrow & 31x& = &5 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{5}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{5}{31} & & \\ & V = \left\{ \frac{5}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-5)& = & -4 \color{red}{-} (3-5x) \\\Leftrightarrow & 18x-30& = &-4-3+5x \\\Leftrightarrow & 18x \color{red}{-30} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 18x-5x& = &-7+30 \\\Leftrightarrow & 13x& = &23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-6)& = & -2 \color{red}{+} (-1+3x) \\\Leftrightarrow & 4x-24& = &-2-1+3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 4x-3x& = &-3+24 \\\Leftrightarrow & x& = &21 \\ & V = \left\{ 21 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+2)& = & 2 \color{red}{-} (-10-5x) \\\Leftrightarrow & -36x+12& = &2+10+5x \\\Leftrightarrow & -36x \color{red}{+12} & = &12 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -36x-5x& = &12-12 \\\Leftrightarrow & -41x& = &0 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{0}{ \color{red}{-41} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-2)& = & -12 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-10& = &-12-15+x \\\Leftrightarrow & 30x \color{red}{-10} & = &-27 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 30x-x& = &-27+10 \\\Leftrightarrow & 29x& = &-17 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-17}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-17}{29} & & \\ & V = \left\{ \frac{-17}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x-4)& = & 7 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x-24& = &7+12-x \\\Leftrightarrow & -12x \color{red}{-24} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &19+24 \\\Leftrightarrow & -11x& = &43 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{43}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-43}{11} & & \\ & V = \left\{ \frac{-43}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+6)& = & -1 \color{red}{-} (-2-5x) \\\Leftrightarrow & 8x+12& = &-1+2+5x \\\Leftrightarrow & 8x \color{red}{+12} & = &1 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 8x-5x& = &1-12 \\\Leftrightarrow & 3x& = &-11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x-6)& = & 9 \color{red}{+} (11-5x) \\\Leftrightarrow & -16x-24& = &9+11-5x \\\Leftrightarrow & -16x \color{red}{-24} & = &20 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -16x+5x& = &20+24 \\\Leftrightarrow & -11x& = &44 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{44}{ \color{red}{-11} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+1)& = & -2 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x+6& = &-2-9+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-11-6 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-3)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & 12x-9& = &3-6-x \\\Leftrightarrow & 12x \color{red}{-9} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &-3+9 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-6)& = & -2 \color{red}{+} (-14+x) \\\Leftrightarrow & 6x-36& = &-2-14+x \\\Leftrightarrow & 6x \color{red}{-36} & = &-16 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 6x-x& = &-16+36 \\\Leftrightarrow & 5x& = &20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{20}{ \color{red}{5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x+5)& = & -9 \color{red}{+} (3+x) \\\Leftrightarrow & -6x+15& = &-9+3+x \\\Leftrightarrow & -6x \color{red}{+15} & = &-6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -6x-x& = &-6-15 \\\Leftrightarrow & -7x& = &-21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-21}{ \color{red}{-7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)