Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

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