Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -30x+\frac{18}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+126} & = & \color{red}{-245x} +20 \\\Leftrightarrow & -1050x \color{red}{+126} \color{blue}{-126} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{-126} \\\Leftrightarrow & -1050x+245x& = & 20-126 \\\Leftrightarrow & \color{red}{-805} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{-805} & & \\\Leftrightarrow & x = \frac{106}{805} & & \\ & V = \left\{ \frac{106}{805} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{-45} & = & \color{red}{84x} +16 \\\Leftrightarrow & -108x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +16 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & -108x-84x& = & 16+45 \\\Leftrightarrow & \color{red}{-192} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-192} & & \\\Leftrightarrow & x = \frac{-61}{192} & & \\ & V = \left\{ \frac{-61}{192} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{11})& = & -5x+\frac{5}{4} \\\Leftrightarrow & -24x-\frac{12}{11}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1056}{ \color{blue}{44} }x- \frac{48}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1056x \color{red}{-48} & = & \color{red}{-220x} +55 \\\Leftrightarrow & -1056x \color{red}{-48} \color{blue}{+48} \color{blue}{+220x} & = & \color{red}{-220x} +55 \color{blue}{+220x} \color{blue}{+48} \\\Leftrightarrow & -1056x+220x& = & 55+48 \\\Leftrightarrow & \color{red}{-836} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-836} & & \\\Leftrightarrow & x = \frac{-103}{836} & & \\ & V = \left\{ \frac{-103}{836} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{15}{8}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{864}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 864x \color{red}{-135} & = & \color{red}{-360x} +64 \\\Leftrightarrow & 864x \color{red}{-135} \color{blue}{+135} \color{blue}{+360x} & = & \color{red}{-360x} +64 \color{blue}{+360x} \color{blue}{+135} \\\Leftrightarrow & 864x+360x& = & 64+135 \\\Leftrightarrow & \color{red}{1224} x& = & 199 \\\Leftrightarrow & x = \frac{199}{1224} & & \\ & V = \left\{ \frac{199}{1224} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{120}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+120} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -1050x \color{red}{+120} \color{blue}{-120} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-120} \\\Leftrightarrow & -1050x+245x& = & 28-120 \\\Leftrightarrow & \color{red}{-805} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{-805} & & \\\Leftrightarrow & x = \frac{4}{35} & & \\ & V = \left\{ \frac{4}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{9})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 28x-\frac{35}{9}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{-385} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 2772x \color{red}{-385} \color{blue}{+385} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+385} \\\Leftrightarrow & 2772x+297x& = & 18+385 \\\Leftrightarrow & \color{red}{3069} x& = & 403 \\\Leftrightarrow & x = \frac{403}{3069} & & \\\Leftrightarrow & x = \frac{13}{99} & & \\ & V = \left\{ \frac{13}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{8}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{105x} +20 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-24} \\\Leftrightarrow & 150x-105x& = & 20-24 \\\Leftrightarrow & \color{red}{45} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{8})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{15}{8}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{144}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 144x \color{red}{+45} & = & \color{red}{120x} +32 \\\Leftrightarrow & 144x \color{red}{+45} \color{blue}{-45} \color{blue}{-120x} & = & \color{red}{120x} +32 \color{blue}{-120x} \color{blue}{-45} \\\Leftrightarrow & 144x-120x& = & 32-45 \\\Leftrightarrow & \color{red}{24} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{24} & & \\ & V = \left\{ \frac{-13}{24} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-88} & = & \color{red}{495x} +63 \\\Leftrightarrow & 792x \color{red}{-88} \color{blue}{+88} \color{blue}{-495x} & = & \color{red}{495x} +63 \color{blue}{-495x} \color{blue}{+88} \\\Leftrightarrow & 792x-495x& = & 63+88 \\\Leftrightarrow & \color{red}{297} x& = & 151 \\\Leftrightarrow & x = \frac{151}{297} & & \\ & V = \left\{ \frac{151}{297} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{+63} & = & \color{red}{-48x} +80 \\\Leftrightarrow & 840x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +80 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & 840x+48x& = & 80-63 \\\Leftrightarrow & \color{red}{888} x& = & 17 \\\Leftrightarrow & x = \frac{17}{888} & & \\ & V = \left\{ \frac{17}{888} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-180} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -1260x \color{red}{-180} \color{blue}{+180} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+180} \\\Leftrightarrow & -1260x+441x& = & 14+180 \\\Leftrightarrow & \color{red}{-819} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-819} & & \\\Leftrightarrow & x = \frac{-194}{819} & & \\ & V = \left\{ \frac{-194}{819} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{9})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -12x-\frac{8}{9}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-16} & = & \color{red}{90x} +21 \\\Leftrightarrow & -216x \color{red}{-16} \color{blue}{+16} \color{blue}{-90x} & = & \color{red}{90x} +21 \color{blue}{-90x} \color{blue}{+16} \\\Leftrightarrow & -216x-90x& = & 21+16 \\\Leftrightarrow & \color{red}{-306} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-306} & & \\\Leftrightarrow & x = \frac{-37}{306} & & \\ & V = \left\{ \frac{-37}{306} \right\} & \\\end{align}\)