Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+5)& = & 6 \color{red}{+} (2+x) \\\Leftrightarrow & 12x+20& = &6+2+x \\\Leftrightarrow & 12x \color{red}{+20} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 12x-x& = &8-20 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-7)& = & -4 \color{red}{+} (8+x) \\\Leftrightarrow & 18x-21& = &-4+8+x \\\Leftrightarrow & 18x \color{red}{-21} & = &4 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &4+21 \\\Leftrightarrow & 17x& = &25 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{25}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{25}{17} & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+6)& = & -12 \color{red}{-} (4+x) \\\Leftrightarrow & -24x+36& = &-12-4-x \\\Leftrightarrow & -24x \color{red}{+36} & = &-16 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -24x+x& = &-16-36 \\\Leftrightarrow & -23x& = &-52 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-52}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{52}{23} & & \\ & V = \left\{ \frac{52}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x-6)& = & -2 \color{red}{+} (-10+x) \\\Leftrightarrow & 36x-36& = &-2-10+x \\\Leftrightarrow & 36x \color{red}{-36} & = &-12 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 36x-x& = &-12+36 \\\Leftrightarrow & 35x& = &24 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{24}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{24}{35} & & \\ & V = \left\{ \frac{24}{35} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x+2)& = & 8 \color{red}{-} (13+3x) \\\Leftrightarrow & -10x+4& = &8-13-3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -10x+3x& = &-5-4 \\\Leftrightarrow & -7x& = &-9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x-3)& = & -12 \color{red}{-} (3+3x) \\\Leftrightarrow & 20x-12& = &-12-3-3x \\\Leftrightarrow & 20x \color{red}{-12} & = &-15 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 20x+3x& = &-15+12 \\\Leftrightarrow & 23x& = &-3 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-3}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x+6)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & 4x+24& = &9+6+x \\\Leftrightarrow & 4x \color{red}{+24} & = &15 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 4x-x& = &15-24 \\\Leftrightarrow & 3x& = &-9 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-9}{ \color{red}{3} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-5)& = & 15 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x-10& = &15-13+x \\\Leftrightarrow & 12x \color{red}{-10} & = &2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 12x-x& = &2+10 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x-4)& = & 10 \color{red}{+} (8-5x) \\\Leftrightarrow & -6x-12& = &10+8-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &18 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &18+12 \\\Leftrightarrow & -x& = &30 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{30}{ \color{red}{-1} } \\\Leftrightarrow & x = -30 & & \\ & V = \left\{ -30 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x-4)& = & -12 \color{red}{+} (6+x) \\\Leftrightarrow & 15x-20& = &-12+6+x \\\Leftrightarrow & 15x \color{red}{-20} & = &-6 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 15x-x& = &-6+20 \\\Leftrightarrow & 14x& = &14 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{14}{ \color{red}{14} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x-3)& = & 10 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x-9& = &10+11-x \\\Leftrightarrow & 12x \color{red}{-9} & = &21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &21+9 \\\Leftrightarrow & 13x& = &30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-5)& = & 8 \color{red}{-} (-15+x) \\\Leftrightarrow & 18x-15& = &8+15-x \\\Leftrightarrow & 18x \color{red}{-15} & = &23 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 18x+x& = &23+15 \\\Leftrightarrow & 19x& = &38 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{38}{ \color{red}{19} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)