Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x+2)& = & -10 \color{red}{-} (10-2x) \\\Leftrightarrow & 5x+10& = &-10-10+2x \\\Leftrightarrow & 5x \color{red}{+10} & = &-20 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-20 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 5x-2x& = &-20-10 \\\Leftrightarrow & 3x& = &-30 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-30}{ \color{red}{3} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+1)& = & -2 \color{red}{-} (9-3x) \\\Leftrightarrow & -4x+2& = &-2-9+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &-11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &-11-2 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-1)& = & 14 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-4& = &14-2+x \\\Leftrightarrow & -12x \color{red}{-4} & = &12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &12+4 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-3)& = & -1 \color{red}{+} (-10-2x) \\\Leftrightarrow & 25x-15& = &-1-10-2x \\\Leftrightarrow & 25x \color{red}{-15} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 25x+2x& = &-11+15 \\\Leftrightarrow & 27x& = &4 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{4}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+6)& = & 9 \color{red}{-} (-14-5x) \\\Leftrightarrow & 36x+36& = &9+14+5x \\\Leftrightarrow & 36x \color{red}{+36} & = &23 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & 36x-5x& = &23-36 \\\Leftrightarrow & 31x& = &-13 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-13}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-13}{31} & & \\ & V = \left\{ \frac{-13}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x+1)& = & 12 \color{red}{+} (15+x) \\\Leftrightarrow & -6x+2& = &12+15+x \\\Leftrightarrow & -6x \color{red}{+2} & = &27 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -6x-x& = &27-2 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x-5)& = & 7 \color{red}{-} (-2-5x) \\\Leftrightarrow & 16x-20& = &7+2+5x \\\Leftrightarrow & 16x \color{red}{-20} & = &9 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & 16x-5x& = &9+20 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+3)& = & -10 \color{red}{+} (-12-5x) \\\Leftrightarrow & -18x+9& = &-10-12-5x \\\Leftrightarrow & -18x \color{red}{+9} & = &-22 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -18x+5x& = &-22-9 \\\Leftrightarrow & -13x& = &-31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-1)& = & -11 \color{red}{+} (-9-2x) \\\Leftrightarrow & 9x-3& = &-11-9-2x \\\Leftrightarrow & 9x \color{red}{-3} & = &-20 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 9x+2x& = &-20+3 \\\Leftrightarrow & 11x& = &-17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+6)& = & -14 \color{red}{-} (-11+x) \\\Leftrightarrow & 8x+24& = &-14+11-x \\\Leftrightarrow & 8x \color{red}{+24} & = &-3 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 8x+x& = &-3-24 \\\Leftrightarrow & 9x& = &-27 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-27}{ \color{red}{9} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x-4)& = & 13 \color{red}{-} (15+3x) \\\Leftrightarrow & 16x-16& = &13-15-3x \\\Leftrightarrow & 16x \color{red}{-16} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 16x+3x& = &-2+16 \\\Leftrightarrow & 19x& = &14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-2)& = & -7 \color{red}{-} (-1+x) \\\Leftrightarrow & 24x-12& = &-7+1-x \\\Leftrightarrow & 24x \color{red}{-12} & = &-6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &-6+12 \\\Leftrightarrow & 25x& = &6 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{6}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)