Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-1)& = & -5 \color{red}{-} (9+x) \\\Leftrightarrow & -12x-6& = &-5-9-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-14+6 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+4)& = & -2 \color{red}{-} (-4-4x) \\\Leftrightarrow & -25x+20& = &-2+4+4x \\\Leftrightarrow & -25x \color{red}{+20} & = &2 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -25x-4x& = &2-20 \\\Leftrightarrow & -29x& = &-18 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-18}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{18}{29} & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x+6)& = & 14 \color{red}{+} (9+x) \\\Leftrightarrow & -30x+30& = &14+9+x \\\Leftrightarrow & -30x \color{red}{+30} & = &23 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &23-30 \\\Leftrightarrow & -31x& = &-7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{7}{31} & & \\ & V = \left\{ \frac{7}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+1)& = & 15 \color{red}{-} (-15-3x) \\\Leftrightarrow & 4x+4& = &15+15+3x \\\Leftrightarrow & 4x \color{red}{+4} & = &30 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &30 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 4x-3x& = &30-4 \\\Leftrightarrow & x& = &26 \\ & V = \left\{ 26 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+3)& = & 15 \color{red}{-} (9+x) \\\Leftrightarrow & 4x+6& = &15-9-x \\\Leftrightarrow & 4x \color{red}{+6} & = &6 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 4x+x& = &6-6 \\\Leftrightarrow & 5x& = &0 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{0}{ \color{red}{5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-5)& = & -4 \color{red}{-} (7+4x) \\\Leftrightarrow & 9x-15& = &-4-7-4x \\\Leftrightarrow & 9x \color{red}{-15} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 9x+4x& = &-11+15 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-1)& = & -8 \color{red}{+} (-2+2x) \\\Leftrightarrow & 5x-5& = &-8-2+2x \\\Leftrightarrow & 5x \color{red}{-5} & = &-10 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 5x-2x& = &-10+5 \\\Leftrightarrow & 3x& = &-5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+4)& = & 8 \color{red}{+} (-10+x) \\\Leftrightarrow & -12x+16& = &8-10+x \\\Leftrightarrow & -12x \color{red}{+16} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -12x-x& = &-2-16 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+4)& = & 14 \color{red}{+} (11+x) \\\Leftrightarrow & 25x+20& = &14+11+x \\\Leftrightarrow & 25x \color{red}{+20} & = &25 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 25x-x& = &25-20 \\\Leftrightarrow & 24x& = &5 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{5}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{5}{24} & & \\ & V = \left\{ \frac{5}{24} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x+5)& = & 5 \color{red}{+} (-11+x) \\\Leftrightarrow & 6x+15& = &5-11+x \\\Leftrightarrow & 6x \color{red}{+15} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 6x-x& = &-6-15 \\\Leftrightarrow & 5x& = &-21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+1)& = & 9 \color{red}{+} (4-5x) \\\Leftrightarrow & 6x+3& = &9+4-5x \\\Leftrightarrow & 6x \color{red}{+3} & = &13 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 6x+5x& = &13-3 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x-2)& = & -7 \color{red}{+} (-7+3x) \\\Leftrightarrow & -20x-8& = &-7-7+3x \\\Leftrightarrow & -20x \color{red}{-8} & = &-14 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -20x-3x& = &-14+8 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)