Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{-160} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 480x \color{red}{-160} \color{blue}{+160} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+160} \\\Leftrightarrow & 480x+72x& = & 21+160 \\\Leftrightarrow & \color{red}{552} x& = & 181 \\\Leftrightarrow & x = \frac{181}{552} & & \\ & V = \left\{ \frac{181}{552} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{7})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & 140x+21x& = & 10+20 \\\Leftrightarrow & \color{red}{161} x& = & 30 \\\Leftrightarrow & x = \frac{30}{161} & & \\ & V = \left\{ \frac{30}{161} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{8}{9}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-56} & = & \color{red}{-441x} +54 \\\Leftrightarrow & 1260x \color{red}{-56} \color{blue}{+56} \color{blue}{+441x} & = & \color{red}{-441x} +54 \color{blue}{+441x} \color{blue}{+56} \\\Leftrightarrow & 1260x+441x& = & 54+56 \\\Leftrightarrow & \color{red}{1701} x& = & 110 \\\Leftrightarrow & x = \frac{110}{1701} & & \\ & V = \left\{ \frac{110}{1701} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{3})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{4}{3}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-4} & = & \color{red}{27x} +4 \\\Leftrightarrow & 30x \color{red}{-4} \color{blue}{+4} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{+4} \\\Leftrightarrow & 30x-27x& = & 4+4 \\\Leftrightarrow & \color{red}{3} x& = & 8 \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{1}{3})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -14x-\frac{7}{3}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x- \frac{14}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{-14} & = & \color{red}{-18x} +21 \\\Leftrightarrow & -84x \color{red}{-14} \color{blue}{+14} \color{blue}{+18x} & = & \color{red}{-18x} +21 \color{blue}{+18x} \color{blue}{+14} \\\Leftrightarrow & -84x+18x& = & 21+14 \\\Leftrightarrow & \color{red}{-66} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-66} & & \\\Leftrightarrow & x = \frac{-35}{66} & & \\ & V = \left\{ \frac{-35}{66} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -9x-\frac{6}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x- \frac{48}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{-48} & = & \color{red}{440x} +99 \\\Leftrightarrow & -792x \color{red}{-48} \color{blue}{+48} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{+48} \\\Leftrightarrow & -792x-440x& = & 99+48 \\\Leftrightarrow & \color{red}{-1232} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-1232} & & \\\Leftrightarrow & x = \frac{-21}{176} & & \\ & V = \left\{ \frac{-21}{176} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-32} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 168x \color{red}{-32} \color{blue}{+32} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+32} \\\Leftrightarrow & 168x+70x& = & 63+32 \\\Leftrightarrow & \color{red}{238} x& = & 95 \\\Leftrightarrow & x = \frac{95}{238} & & \\ & V = \left\{ \frac{95}{238} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{1}{2})& = & -3x+\frac{7}{5} \\\Leftrightarrow & -14x-\frac{7}{2}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x- \frac{35}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{-35} & = & \color{red}{-30x} +14 \\\Leftrightarrow & -140x \color{red}{-35} \color{blue}{+35} \color{blue}{+30x} & = & \color{red}{-30x} +14 \color{blue}{+30x} \color{blue}{+35} \\\Leftrightarrow & -140x+30x& = & 14+35 \\\Leftrightarrow & \color{red}{-110} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-110} & & \\\Leftrightarrow & x = \frac{-49}{110} & & \\ & V = \left\{ \frac{-49}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+14} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 42x \color{red}{+14} \color{blue}{-14} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-14} \\\Leftrightarrow & 42x+15x& = & 8-14 \\\Leftrightarrow & \color{red}{57} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{57} & & \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{8}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-88} & = & \color{red}{-165x} +50 \\\Leftrightarrow & -1100x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & -1100x+165x& = & 50+88 \\\Leftrightarrow & \color{red}{-935} x& = & 138 \\\Leftrightarrow & x = \frac{138}{-935} & & \\\Leftrightarrow & x = \frac{-138}{935} & & \\ & V = \left\{ \frac{-138}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{9})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 14x-\frac{14}{9}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1386}{ \color{blue}{99} }x- \frac{154}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1386x \color{red}{-154} & = & \color{red}{495x} +90 \\\Leftrightarrow & 1386x \color{red}{-154} \color{blue}{+154} \color{blue}{-495x} & = & \color{red}{495x} +90 \color{blue}{-495x} \color{blue}{+154} \\\Leftrightarrow & 1386x-495x& = & 90+154 \\\Leftrightarrow & \color{red}{891} x& = & 244 \\\Leftrightarrow & x = \frac{244}{891} & & \\ & V = \left\{ \frac{244}{891} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{-10} & = & \color{red}{-35x} +8 \\\Leftrightarrow & 28x \color{red}{-10} \color{blue}{+10} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+10} \\\Leftrightarrow & 28x+35x& = & 8+10 \\\Leftrightarrow & \color{red}{63} x& = & 18 \\\Leftrightarrow & x = \frac{18}{63} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)