Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x+2)& = & 8 \color{red}{+} (4+3x) \\\Leftrightarrow & -10x+4& = &8+4+3x \\\Leftrightarrow & -10x \color{red}{+4} & = &12 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -10x-3x& = &12-4 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-4)& = & 7 \color{red}{+} (2+3x) \\\Leftrightarrow & -4x-16& = &7+2+3x \\\Leftrightarrow & -4x \color{red}{-16} & = &9 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -4x-3x& = &9+16 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x-3)& = & 14 \color{red}{+} (1+x) \\\Leftrightarrow & -8x-12& = &14+1+x \\\Leftrightarrow & -8x \color{red}{-12} & = &15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &15+12 \\\Leftrightarrow & -9x& = &27 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{27}{ \color{red}{-9} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x-5)& = & -5 \color{red}{-} (-11+x) \\\Leftrightarrow & -6x-15& = &-5+11-x \\\Leftrightarrow & -6x \color{red}{-15} & = &6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -6x+x& = &6+15 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+6)& = & -2 \color{red}{-} (-13+x) \\\Leftrightarrow & -30x+30& = &-2+13-x \\\Leftrightarrow & -30x \color{red}{+30} & = &11 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &11-30 \\\Leftrightarrow & -29x& = &-19 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-19}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{19}{29} & & \\ & V = \left\{ \frac{19}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x+4)& = & 10 \color{red}{+} (13-3x) \\\Leftrightarrow & 4x+16& = &10+13-3x \\\Leftrightarrow & 4x \color{red}{+16} & = &23 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & 4x+3x& = &23-16 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x-3)& = & 3 \color{red}{-} (1-3x) \\\Leftrightarrow & 4x-6& = &3-1+3x \\\Leftrightarrow & 4x \color{red}{-6} & = &2 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 4x-3x& = &2+6 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+2)& = & 8 \color{red}{+} (-10+x) \\\Leftrightarrow & -12x+8& = &8-10+x \\\Leftrightarrow & -12x \color{red}{+8} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &-2-8 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+6)& = & -11 \color{red}{+} (-1+x) \\\Leftrightarrow & -36x+36& = &-11-1+x \\\Leftrightarrow & -36x \color{red}{+36} & = &-12 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -36x-x& = &-12-36 \\\Leftrightarrow & -37x& = &-48 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-48}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{48}{37} & & \\ & V = \left\{ \frac{48}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x+1)& = & -15 \color{red}{-} (2+x) \\\Leftrightarrow & -20x+4& = &-15-2-x \\\Leftrightarrow & -20x \color{red}{+4} & = &-17 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -20x+x& = &-17-4 \\\Leftrightarrow & -19x& = &-21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-2)& = & -10 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-4& = &-10+7-x \\\Leftrightarrow & 12x \color{red}{-4} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &-3+4 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x+5)& = & -7 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x+30& = &-7-15+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-22 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-22-30 \\\Leftrightarrow & -31x& = &-52 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-52}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{52}{31} & & \\ & V = \left\{ \frac{52}{31} \right\} & \\\end{align}\)