Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-6)& = & -15 \color{red}{+} (13+3x) \\\Leftrightarrow & 16x-24& = &-15+13+3x \\\Leftrightarrow & 16x \color{red}{-24} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 16x-3x& = &-2+24 \\\Leftrightarrow & 13x& = &22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-1)& = & 10 \color{red}{-} (-3+x) \\\Leftrightarrow & -8x-4& = &10+3-x \\\Leftrightarrow & -8x \color{red}{-4} & = &13 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -8x+x& = &13+4 \\\Leftrightarrow & -7x& = &17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x-5)& = & 13 \color{red}{+} (-12+x) \\\Leftrightarrow & -24x-30& = &13-12+x \\\Leftrightarrow & -24x \color{red}{-30} & = &1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -24x-x& = &1+30 \\\Leftrightarrow & -25x& = &31 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{31}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-31}{25} & & \\ & V = \left\{ \frac{-31}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x+6)& = & -6 \color{red}{-} (4+3x) \\\Leftrightarrow & -2x+12& = &-6-4-3x \\\Leftrightarrow & -2x \color{red}{+12} & = &-10 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -2x+3x& = &-10-12 \\\Leftrightarrow & x& = &-22 \\ & V = \left\{ -22 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x-5)& = & -5 \color{red}{+} (11-2x) \\\Leftrightarrow & 5x-25& = &-5+11-2x \\\Leftrightarrow & 5x \color{red}{-25} & = &6 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & 5x+2x& = &6+25 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-7)& = & 4 \color{red}{-} (-10+x) \\\Leftrightarrow & 30x-42& = &4+10-x \\\Leftrightarrow & 30x \color{red}{-42} & = &14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 30x+x& = &14+42 \\\Leftrightarrow & 31x& = &56 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{56}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{56}{31} & & \\ & V = \left\{ \frac{56}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x+4)& = & 3 \color{red}{+} (-4+x) \\\Leftrightarrow & -8x+8& = &3-4+x \\\Leftrightarrow & -8x \color{red}{+8} & = &-1 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &-1-8 \\\Leftrightarrow & -9x& = &-9 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-9}{ \color{red}{-9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+1)& = & -6 \color{red}{-} (3+3x) \\\Leftrightarrow & 16x+4& = &-6-3-3x \\\Leftrightarrow & 16x \color{red}{+4} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 16x+3x& = &-9-4 \\\Leftrightarrow & 19x& = &-13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x+7)& = & -1 \color{red}{+} (14+x) \\\Leftrightarrow & 8x+28& = &-1+14+x \\\Leftrightarrow & 8x \color{red}{+28} & = &13 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 8x-x& = &13-28 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+7)& = & -9 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+14& = &-9+6+x \\\Leftrightarrow & -12x \color{red}{+14} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -12x-x& = &-3-14 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+6)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & 6x+36& = &-13+6-x \\\Leftrightarrow & 6x \color{red}{+36} & = &-7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 6x+x& = &-7-36 \\\Leftrightarrow & 7x& = &-43 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-43}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-43}{7} & & \\ & V = \left\{ \frac{-43}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+6)& = & 9 \color{red}{-} (-2+x) \\\Leftrightarrow & -15x+18& = &9+2-x \\\Leftrightarrow & -15x \color{red}{+18} & = &11 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -15x+x& = &11-18 \\\Leftrightarrow & -14x& = &-7 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-7}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)