Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{4}{9})& = & -6x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{28}{9}& = & -6x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-308} & = & \color{red}{-594x} +54 \\\Leftrightarrow & 3465x \color{red}{-308} \color{blue}{+308} \color{blue}{+594x} & = & \color{red}{-594x} +54 \color{blue}{+594x} \color{blue}{+308} \\\Leftrightarrow & 3465x+594x& = & 54+308 \\\Leftrightarrow & \color{red}{4059} x& = & 362 \\\Leftrightarrow & x = \frac{362}{4059} & & \\ & V = \left\{ \frac{362}{4059} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{441x} +56 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & 504x-441x& = & 56-54 \\\Leftrightarrow & \color{red}{63} x& = & 2 \\\Leftrightarrow & x = \frac{2}{63} & & \\ & V = \left\{ \frac{2}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-2)& = & 5x+\frac{7}{6} \\\Leftrightarrow & -14x+14& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 1 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{84}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+84} & = & \color{red}{30x} +7 \\\Leftrightarrow & -84x \color{red}{+84} \color{blue}{-84} \color{blue}{-30x} & = & \color{red}{30x} +7 \color{blue}{-30x} \color{blue}{-84} \\\Leftrightarrow & -84x-30x& = & 7-84 \\\Leftrightarrow & \color{red}{-114} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{-114} & & \\\Leftrightarrow & x = \frac{77}{114} & & \\ & V = \left\{ \frac{77}{114} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -6x+\frac{10}{3}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-144}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -144x \color{red}{+80} & = & \color{red}{168x} +9 \\\Leftrightarrow & -144x \color{red}{+80} \color{blue}{-80} \color{blue}{-168x} & = & \color{red}{168x} +9 \color{blue}{-168x} \color{blue}{-80} \\\Leftrightarrow & -144x-168x& = & 9-80 \\\Leftrightarrow & \color{red}{-312} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-312} & & \\\Leftrightarrow & x = \frac{71}{312} & & \\ & V = \left\{ \frac{71}{312} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{10})& = & 4x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{9}{10}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1350}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{360}{ \color{blue}{90} }x+ \frac{100}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1350x \color{red}{-81} & = & \color{red}{360x} +100 \\\Leftrightarrow & 1350x \color{red}{-81} \color{blue}{+81} \color{blue}{-360x} & = & \color{red}{360x} +100 \color{blue}{-360x} \color{blue}{+81} \\\Leftrightarrow & 1350x-360x& = & 100+81 \\\Leftrightarrow & \color{red}{990} x& = & 181 \\\Leftrightarrow & x = \frac{181}{990} & & \\ & V = \left\{ \frac{181}{990} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & 9x+\frac{7}{11} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-330} & = & \color{red}{693x} +49 \\\Leftrightarrow & -1386x \color{red}{-330} \color{blue}{+330} \color{blue}{-693x} & = & \color{red}{693x} +49 \color{blue}{-693x} \color{blue}{+330} \\\Leftrightarrow & -1386x-693x& = & 49+330 \\\Leftrightarrow & \color{red}{-2079} x& = & 379 \\\Leftrightarrow & x = \frac{379}{-2079} & & \\\Leftrightarrow & x = \frac{-379}{2079} & & \\ & V = \left\{ \frac{-379}{2079} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-12} & = & \color{red}{40x} +6 \\\Leftrightarrow & -75x \color{red}{-12} \color{blue}{+12} \color{blue}{-40x} & = & \color{red}{40x} +6 \color{blue}{-40x} \color{blue}{+12} \\\Leftrightarrow & -75x-40x& = & 6+12 \\\Leftrightarrow & \color{red}{-115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-115} & & \\\Leftrightarrow & x = \frac{-18}{115} & & \\ & V = \left\{ \frac{-18}{115} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{2})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -12x+\frac{15}{2}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-24}{ \color{blue}{2} }x+ \frac{15}{ \color{blue}{2} })& = & (\frac{10}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -24x \color{red}{+15} & = & \color{red}{10x} +7 \\\Leftrightarrow & -24x \color{red}{+15} \color{blue}{-15} \color{blue}{-10x} & = & \color{red}{10x} +7 \color{blue}{-10x} \color{blue}{-15} \\\Leftrightarrow & -24x-10x& = & 7-15 \\\Leftrightarrow & \color{red}{-34} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-34} & & \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{3}{11} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+154} & = & \color{red}{264x} +9 \\\Leftrightarrow & -693x \color{red}{+154} \color{blue}{-154} \color{blue}{-264x} & = & \color{red}{264x} +9 \color{blue}{-264x} \color{blue}{-154} \\\Leftrightarrow & -693x-264x& = & 9-154 \\\Leftrightarrow & \color{red}{-957} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-957} & & \\\Leftrightarrow & x = \frac{5}{33} & & \\ & V = \left\{ \frac{5}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{+165} & = & \color{red}{308x} +24 \\\Leftrightarrow & -440x \color{red}{+165} \color{blue}{-165} \color{blue}{-308x} & = & \color{red}{308x} +24 \color{blue}{-308x} \color{blue}{-165} \\\Leftrightarrow & -440x-308x& = & 24-165 \\\Leftrightarrow & \color{red}{-748} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-748} & & \\\Leftrightarrow & x = \frac{141}{748} & & \\ & V = \left\{ \frac{141}{748} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{-315x} +10 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{+84} \\\Leftrightarrow & -280x+315x& = & 10+84 \\\Leftrightarrow & \color{red}{35} x& = & 94 \\\Leftrightarrow & x = \frac{94}{35} & & \\ & V = \left\{ \frac{94}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+16} & = & \color{red}{42x} +21 \\\Leftrightarrow & -96x \color{red}{+16} \color{blue}{-16} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{-16} \\\Leftrightarrow & -96x-42x& = & 21-16 \\\Leftrightarrow & \color{red}{-138} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-138} & & \\\Leftrightarrow & x = \frac{-5}{138} & & \\ & V = \left\{ \frac{-5}{138} \right\} & \\\end{align}\)