Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 30x-\frac{30}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-210} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 2310x \color{red}{-210} \color{blue}{+210} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+210} \\\Leftrightarrow & 2310x+539x& = & 88+210 \\\Leftrightarrow & \color{red}{2849} x& = & 298 \\\Leftrightarrow & x = \frac{298}{2849} & & \\ & V = \left\{ \frac{298}{2849} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{+12} & = & \color{red}{126x} +35 \\\Leftrightarrow & 56x \color{red}{+12} \color{blue}{-12} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-12} \\\Leftrightarrow & 56x-126x& = & 35-12 \\\Leftrightarrow & \color{red}{-70} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-70} & & \\\Leftrightarrow & x = \frac{-23}{70} & & \\ & V = \left\{ \frac{-23}{70} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+24} & = & \color{red}{-80x} +25 \\\Leftrightarrow & -180x \color{red}{+24} \color{blue}{-24} \color{blue}{+80x} & = & \color{red}{-80x} +25 \color{blue}{+80x} \color{blue}{-24} \\\Leftrightarrow & -180x+80x& = & 25-24 \\\Leftrightarrow & \color{red}{-100} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-100} & & \\\Leftrightarrow & x = \frac{-1}{100} & & \\ & V = \left\{ \frac{-1}{100} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+36} & = & \color{red}{165x} +22 \\\Leftrightarrow & -396x \color{red}{+36} \color{blue}{-36} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{-36} \\\Leftrightarrow & -396x-165x& = & 22-36 \\\Leftrightarrow & \color{red}{-561} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-561} & & \\\Leftrightarrow & x = \frac{14}{561} & & \\ & V = \left\{ \frac{14}{561} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{7})& = & -4x+\frac{5}{6} \\\Leftrightarrow & 9x+\frac{12}{7}& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{378}{ \color{blue}{42} }x+ \frac{72}{ \color{blue}{42} })& = & (\frac{-168}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 378x \color{red}{+72} & = & \color{red}{-168x} +35 \\\Leftrightarrow & 378x \color{red}{+72} \color{blue}{-72} \color{blue}{+168x} & = & \color{red}{-168x} +35 \color{blue}{+168x} \color{blue}{-72} \\\Leftrightarrow & 378x+168x& = & 35-72 \\\Leftrightarrow & \color{red}{546} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{546} & & \\ & V = \left\{ \frac{-37}{546} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 6x+\frac{10}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+10} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 42x \color{red}{+10} \color{blue}{-10} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-10} \\\Leftrightarrow & 42x+35x& = & 10-10 \\\Leftrightarrow & \color{red}{77} x& = & 0 \\\Leftrightarrow & x = \frac{0}{77} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{231x} +110 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-90} \\\Leftrightarrow & -990x-231x& = & 110-90 \\\Leftrightarrow & \color{red}{-1221} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-1221} & & \\\Leftrightarrow & x = \frac{-20}{1221} & & \\ & V = \left\{ \frac{-20}{1221} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{+20} & = & \color{red}{6x} +10 \\\Leftrightarrow & 45x \color{red}{+20} \color{blue}{-20} \color{blue}{-6x} & = & \color{red}{6x} +10 \color{blue}{-6x} \color{blue}{-20} \\\Leftrightarrow & 45x-6x& = & 10-20 \\\Leftrightarrow & \color{red}{39} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{39} & & \\ & V = \left\{ \frac{-10}{39} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{9})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+88} & = & \color{red}{-495x} +72 \\\Leftrightarrow & 594x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +72 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & 594x+495x& = & 72-88 \\\Leftrightarrow & \color{red}{1089} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{1089} & & \\ & V = \left\{ \frac{-16}{1089} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & 8x+\frac{8}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{120x} +24 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & 315x-120x& = & 24-70 \\\Leftrightarrow & \color{red}{195} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{195} & & \\ & V = \left\{ \frac{-46}{195} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -6x-\frac{4}{5}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{-315x} +25 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{+315x} & = & \color{red}{-315x} +25 \color{blue}{+315x} \color{blue}{+36} \\\Leftrightarrow & -270x+315x& = & 25+36 \\\Leftrightarrow & \color{red}{45} x& = & 61 \\\Leftrightarrow & x = \frac{61}{45} & & \\ & V = \left\{ \frac{61}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{15}{4}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+75} & = & \color{red}{140x} +24 \\\Leftrightarrow & -400x \color{red}{+75} \color{blue}{-75} \color{blue}{-140x} & = & \color{red}{140x} +24 \color{blue}{-140x} \color{blue}{-75} \\\Leftrightarrow & -400x-140x& = & 24-75 \\\Leftrightarrow & \color{red}{-540} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-540} & & \\\Leftrightarrow & x = \frac{17}{180} & & \\ & V = \left\{ \frac{17}{180} \right\} & \\\end{align}\)